Show that there is no cubic curve for which the tangent lines at two distinct points coincide.

Show that the family of curves for which the slope of the tangent at any point (x,y) on its (x^(2) + y^(2))/(2xy) , is given by x^(2) - y^(2) = cx .

Show that the curve for which the normal at every point passes through a fixed point is a circle.

Find the points on the curve y=x^3-2x^2-x at which the tangent lines are parallel to the line y=3x-2

A Tangent to a circle is a line which touches the circle at only one point.

Find a point on the curve y = (x – 2)^(2) at which the tangent is parallel to the chord joining the points (2, 0) and (4, 4).

The number of line/s passing through two distinct points is ........ .

Show that the angle between the tangent at any point P and the line joining P to the origin O is same at all points on the curve log(x^2+y^2)=ktan^(-1)(y/x)

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.