Find the curve for which the length of normal is equal to the radius vector.

The curve for which the length of the normal is equal to the length of the radius vector is/are (a) circles (b) rectangular hyperbola (c) ellipses (d) straight lines

Find the curve for which the perpendicular from the foot of the ordinate to the tangent is of constant length.

At any point on the curve 2x^2y^2-x^4=c , the mean proportional between the abscissa and the difference between the abscissa and the sub-normal drawn to the curve at the same point is equal to (a) ordinate (b) radius vector (c) x-intercept of tangent (d) sub-tangent

The angle subtended at the centre of a circle , by a chord whose length is equal to the radius of the circle will be

Find the points on the curve y = x^(3) at which the slope of the tangent is equal to the y-coordinate of the point.

Three normals are from the point (c,0) to the curve y^(2)=x . Show that c must be greater than (1)/(2) .One normal is always the x-axis. Find c for which the other two normals are perpendicular to each other.

The curved surface area of a right circular cone is sqrt(5) times of its base area . Find the ratio of the height and the length of radius of the cone.

The volume of a sphere and a right circular cone are same. The height of the cone is twice the length of the radius of the cone. Find the ratio of the curved surface area of the cone and sphere.

on the curved surface of the axis of a globe with the length of 14 cm radius, two circular holes area made each of which has the length of radius 0.7 cm.Calculate the area of metal sheet surrounding its curved surface.

Determine p such that the length of the sub-tangent and sub-normal is equal for the curve y=e^(p x)+p x at the point (0,1)dot