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.

A curve passing through (1, 0) is such that the ratio of the square of the intercept cut by any tangent on the y-axis to the Sub-normal is equal to the ratio of the product of the Coordinates of the point of tangency to the product of square of the slope of the tangent and the subtangent at the same point, is given by

Find the intercepts cut off by the plane 2x+y-z=5

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

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

Statement I The ratio of length of tangent to length of normal is inversely proportional to the ordinate of the point of tengency at the curve y^(2)=4ax . Statement II Length of normal and tangent to a curve y=f(x)" is "|ysqrt(1+m^(2))| and |(ysqrt(1+m^(2)))/(m)| , where m=(dy)/(dx).

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

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

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.

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.