Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance?...

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Chapter 9- Distance and Conics Annie Kane-P6

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Transcript of Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance?...

Page 1: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Chapter 9- Distance and Conics

Annie Kane-P6

Page 2: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

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What’s the distance?

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Page 3: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

What’s the Distance? - for 100

Remember to phrase your answer in the form of a question!

Find the distance between:

(13,6) and (0,6)

Page 4: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

What’s the Distance? - for 100

13

Page 5: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

What’s the Distance? - for 200

Find the midpoint of:

(2, 1) and (-2, 0)

Remember to phrase your answer in the form of a question!

Page 6: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

What’s the Distance? - for 200

(0, ½)

Page 7: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

What’s the Distance? - for 300

Find the (a) distance and (b) midpoint between:

(1+ 5, 2+ 3) and

(1- 5, -2 + 3)

Remember to phrase your answer in the form of a question!

Page 8: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

What’s the Distance? - for 300

a)6

b)(1, 3)

Page 9: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

What’s the Distance? - for 400

The midpoint of the seqment joining A(-2,4) and B is (7,-1) Find B?

Remember to phrase your answer in the form of a question!

Page 10: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

What’s the Distance? - for 400

(16,-6)

Page 11: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

What’s the Distance? - for 500

Find the value(s) of “X” so that the distance between

(-2,4) and (X, 7) is 10.

Remember to phrase your answer in the form of a question!

Page 12: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

What’s the Distance? - for 500

X=

Page 13: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Circles - for 100

Find the (a) radius and (b) center of:

x²+y²+12x-6y=0

Remember to phrase your answer in the form of a question!

Page 14: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Circles - for 100

(a)(-6,3)(b) 35

Page 15: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Circles - for 200

Find the equation of a circle with radius=2 and

center of (-2,3)

Remember to phrase your answer in the form of a question!

Page 16: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Circles - for 200

(x+2)²+(y-3)²=4

Page 17: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Circles - for 300

Find the equation of the circle with a diameter that has endpoints (-5,-3) and

(2,5)

Remember to phrase your answer in the form of a question!

Page 18: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Circles - for 300

(x+3/2) ² + (y-1)²=113/4

Page 19: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Circles - for 400

Graph and find the equation of the circle that is on line y-3=0 and that is

tangent to the x axis at (4,0)

Remember to phrase your answer in the form of a question!

Page 20: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Circles - for 40032

sec(x-4)2 + (y-3)2 =9

Page 21: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Circles - for 500

Find the center and radius of

4x2+4y2-16x-24y+36=0

Remember to phrase your answer in the form of a question!

Page 22: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Circles - for 500

• C(2,3) r=2

Page 23: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Parabolas - for 100

Remember to phrase your answer in the form of a question!

Find the focus when V(4,2) and D:y=-3 are

given

*D=directrix, V= vertex, F=focus

Page 24: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Parabolas - for 100

(4,7)

Page 25: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Parabolas - for 200

Remember to phrase your answer in the form of a question!

Find an equation of a parabola with F(0,0)

and D y=4.

*D=directrix, V= vertex, F=focus

Page 26: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Parabolas - for 200

y-2= -1/8x²

Page 27: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Parabolas - for 300

Remember to phrase your answer in the form of a question!

Find the vertex, focus, and directrix of:

4y²+4y-2x=-2

Page 28: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Parabolas - for 300

V: (1/2, -1/2)

F: (5/8, -1/2)

D: x= 3/8

Page 29: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Parabolas - for 400

Remember to phrase your answer in the form of a question!

Give vertex focus and directrix and Graph the

parabola:

x-1=1/8(y-4)²

Page 30: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Parabolas - for 400

Page 31: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Parabolas - for 500

Remember to phrase your answer in the form of a question!

Find the vertex, which way the parabola opens, the axis of symmetry, focus, and

the directrix of:

X²+10x-4y+21=0

Page 32: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Parabolas - for 500

V (-5,-1)

Opens: Up

Axis of Symmetry: x=-5

Focus (-5,0)

Directrix: y=-2

Page 33: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Ellipses- for 100

Remember to phrase your answer in the form of a question!

What is the formula for finding the foci of an

ellipse?

Page 34: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Ellipses- for 100

a²-c²=b²

Page 35: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Ellipses- for 200

Find the vertices of the ellipse:

25x ²+9y²-150x+36y+36=0

Remember to phrase your answer in the form of a question!

8,2

xx

Page 36: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Ellipses- for 200

(0,-2)

(6, -2)

(3,3)

(3,-7)

Page 37: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Ellipses- for 300

Find the vertices and Graph:

16x²+9y²=144

Remember to phrase your answer in the form of a question!

Page 38: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Ellipses- for 300(0,4) (0,-4)(3,0) (-3,0

Page 39: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Ellipses- for 400

Find an equation of an ellipse with:

x-intercepts: ± 5

and

y-intercepts: ±2

Remember to phrase your answer in the form of a question!

Page 40: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Ellipses- for 400

Page 41: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Ellipses- for 500

Find the equation of an ellipse that is tangent to the x-axis and the y-axis

with center (4, -3)

Remember to phrase your answer in the form of a question!

Page 42: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Ellipses- for 500

Page 43: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Hyperbolas - for 100

Find the foci of the hyperbola:

Remember to phrase your answer in the form of a question!

Page 44: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Hyperbolas - for 100

(0, ±41)

Page 45: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Hyperbolas - for 200

The formula for finding the foci of a hyperbola is…

Remember to phrase your answer in the form of a question!

Page 46: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Hyperbolas - for 200

c²- a²=b²

Page 47: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Hyperbolas - for 300

Remember to phrase your answer in the form of a question!

Find an equation of a hyperbola with the given foci and the difference of

their focal radii:

(5,-9) (5, -1); 6

Page 48: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Hyperbolas - for 300

Page 49: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Hyperbolas - for 400

Graph:

Y= -x²+9

Remember to phrase your answer in the form of a question!

Page 50: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Hyperbolas - for 400

Page 51: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Hyperbolas - for 500

Find the equation of a hyperbola with foci at (-5,1) and (-5,-5) and when the

distance between the vertices is 4.

Remember to phrase your answer in the form of a question!

Page 52: Chapter 9- Distance and Conics Annie Kane-P6. 100 200 300 400 500 What’s the distance? CirclesParabolasEllipsesHyperbolas 100 200 300 400 500 100 200.

Hyperbolas - for 500


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