Lecture #7 analytic geometry
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Transcript of Lecture #7 analytic geometry
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Lecture #7EllipseParts of Ellipse and its graph• Equation of Ellipse
- Standard Equation- General Equation
• Formulas
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ELLIPSEAn ellipse is defined by two points, each called a
focus. If you take any point on the ellipse, the sum of the distances to the focus points is constant.
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PARTS OF AN ELLIPSEVertices – the points at which an ellipse makes its
sharpest turns and lies on the major axis, also end of major axis
Co-vertices – ends of minor axisFocus/foci – point/s that define the ellipse and lies on
the major axisMajor axis – the longest diameter of the ellipseMinor axis – the shortest diameter of the ellipse
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EQUATIONS OF ELLIPSEThe equation of ellipse, if the center is at the origin,
major axis at x-axis, is given by
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EQUATIONS OF ELLIPSEThe equation of ellipse, if the center is at the origin,
major axis at y-axis, is given by
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EQUATIONS OF ELLIPSEThe equation of ellipse, if the center is at (h, k), major
axis parallel to x-axis, is given by
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EQUATIONS OF ELLIPSEThe equation of ellipse, if the center is at (h, k), major
axis parallel to y-axis, is given by
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The general equation of ellipse is given by
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FORMULAS(if center is at the origin and major axis at x-
axis)
Vertices Co-vertices
(a, 0) (-a, 0) (0, b) (0, -b)
Foci Length of LR
(c, 0) (-c, 0)Length of major and minor axis
2a (major) 2b (minor)
Ends of Latera recta
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FORMULAS(if center is at the origin and major axis at y-
axis)
Vertices Co-vertices
(0, a) (0, -a) (b, 0) (-b, 0)
Foci Length of LR
(0, c) (0, -c)Length of major and minor axis
2a (major) 2b (minor)
Ends of Latera recta
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FORMULAS(if center is at (h, k) and major axis at x-axis)
Vertices Co-vertices
(h + a, k) (h - a, k) (h, k + b) (h, k-b)
Foci Length of LR
(h + c, k) (h - c, k)
Length of major and minor axis
2a (major) 2b (minor)
Ends of Latera recta
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FORMULAS(if center is at (h, k) and major axis at y-axis)
Vertices Co-vertices
(h, k + a) (h, k - a) (h + b, k) (h - b, k)
Foci Length of LR
(h, k + c) (h, k - c)
Length of major and minor axis
2a (major) 2b (minor)
Ends of Latera recta
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Sample ProblemGraph the ff. ellipses.