For a curve (length of normal)^2/(length of tangent)^2 is equal to

For the curve y=f(x) prove that (lenght of normal)^2/(lenght of tangent)^2 =length of sub-normal/length of sub-tangent

Find the equation of all possible curves such that length of intercept made by any tangent on x-axis is equal to the square of X-coordinate of the point of tangency. Given that the curve passes through (2,1)

If the length of sub-normal is equal to the length of sub-tangent at any point (3,4) on the curve y=f(x) and the tangent at (3,4) to y=f(x) meets the coordinate axes at Aa n dB , then the maximum area of the triangle O A B , where O is origin, is 45/2 (b) 49/2 (c) 25/2 (d) 81/2

If the length of sub-normal is equal to the length of sub-tangent at any point (3,4) on the curve y=f(x) and the tangent at (3,4) to y=f(x) meets the coordinate axes at Aa n dB , then the maximum area of the triangle O A B , where O is origin, is 45/2 (b) 49/2 (c) 25/2 (d) 81/2

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

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

Find the equation of tangent and normal the length of subtangent and subnormal of the circle x^(2)+y^(2)=a^(2) at the point (x_(1),y_(1)) .

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

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

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