Institute of Engineering & TechnologyB.Tech. I Sem. (2011)Subject: Engineering Mathematics – I

Assignment Sheet -2 Unit: I Topic: CURVATUREDate of tutorial: 18/08/2011

Date of submission:24/08/2011

Q.1. Find the radius of curvature at on the Folium of Descartes, .

Q.2. Prove that the radius of curvature of the cycloid , at points is .

Q.3. Find the radius of curvature at the origin for the curve .

Q.4. Show that the radius of curvature at P on the ellipse is where

CD is the semi-diameter conjugate to CP, C is the center of the ellipse. Q.5. Prove that the coordinates of center of curvature at on the parabola

are .

Q.6. Show that for the curve , there is one point of inflexion at origin and others at .

Q.7. Prove that the radius of curvature at (x,y) on the curve , is given by

.

Q.8. Prove that the radius of curvature at any point on , is .

Q.9. Find the radius of curvature at the origin for the curve .Q.10. Find the radius of curvature at the origin for the curve

.Q.11. Find the point of inflexion on the curve , .Q.12. Show that the chord of curvature through focus of parabola is four times

the focal distance of the point.Q.13. Find the equation of the circle of curvature at origin for the curve

.Q.14. Show that the chord of curvature parallel to y-axis for the catenary

is double the ordinate of the point and the chord parallel to x-axis is of

length .

DEPARTMENT OF MATHEMATICS 2