Find the curve for which area of triangle formed by x-axis, tangent drawn at any point on the curve and radius vector of point of tangency is constant, equal to `a^2`

Find the curve for which the intercept cut off by any tangent on y-axis is proportional to the square of the ordinate of the point of tangency.

The length of subtangent at any point of the curve log y = 25x is

The curve for which the ratio of the length of the segment intercepted by any tangent on the Y-axis to the length of the radius vector is constant (k), is

Area of the triangle formed by the pair of tangents drawn form (1,1) to x^(2)+2x-y+7=0 and its chord of contact is Delta then (Delta)/(9) is equal to

The Curve possessing the property text the intercept made by the tangent at any point of the curve on the y-axis is equal to square of the abscissa of the point of tangency, is given by

Find the family of curves, the subtangent at any point of which is the arithmetic mean of the co-ordinate point of tangency.

The area of the region bounded by the curve y= x^2 +2x +1 , Y- axis and the tangent drawn at a point (1,4) to the curve is ……. Sq . Units

Find the equation of a curve passing through the point (0, -2) given that at any point (x,y) on the curve, the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.

A curve y=f(x) has the property that the perpendicular distance of the origin from the normal at any point P of the curve is equal to the distance of the point P from the x-axis. Then the differential equation of the curve

Find the points on the curve x^(2)y^(2)+xy=2 at which the slope of the tangent is -1 .