If the length of subnormal is equal to length of subtangent at a point (3,4) on the curve y = f(x) and the tangent at (3,4) to y=f(x) meets the coordinate axes at A and B, then find the maximum area of the `DeltaOBB` wherer O is orgin

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 tangent at (1,1) on y^2=x(2-x)^2 meets the curve again at P , then find coordinates of P .

The tangent at any point P on the circle x^2+y^2=4 meets the coordinate axes at A and B . Then find the locus of the midpoint of A Bdot

Find the length of the subtangent to the curve x^2y^2=a^4 at (-a,a).

If length of tangent at any point on the curve y=f(x) intercepted between the point and the x-axis is of length 1 . Find the equation of the curve.

Find the length of tangent to the curve y=4x^3-2x^5 at (-1,1)

Find the point on the curve y=x^3-11 x+5 at which the tangent has the equation y=x-11

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.

Find the point on the curve y = x^(3) – 11x + 5 at which the tangent is y = x – 11.

If the tangent at any point of the curve x^((2)/(3))+y^((2)/(3))=a^((2)/(3)) meets the coordinate axes in A and B, then show that the locus of mid-points of AB is a circle.