The sum of the lengths of tangent and subtangent ata point of `y=alog(x^2-a^2),(agt0)` is proportional to

Find the curve for which the sum of the lengths of the tangent and subtangent at any of its point is proportional to the product of the co-ordinates of the point of tangency, the proportionality factor is equal to k.

Length of the subtangent at any point on y^n=a^(n-1)x is

For the curve y=a ln(x^(2)-a^(2)), show that the sum of length of tangent and sub-tangent at any point is proportional to product of coordinates of point of tangency.

For the curve y=a1n(x^2-a^2) , show that the sum of length of tangent and sub-tangent at any point is proportional to product of coordinates of point of tangency.

For the curve y=a1n(x^2-a^2) , show that the sum of length of tangent and sub-tangent at any point is proportional to product of coordinates of point of tangency.

For the curve y=a1n(x^2-a^2) , show that the sum of length of tangent and sub-tangent at any point is proportional to product of coordinates of point of tangency.

For the curve y=a1n(x^2-a^2) , show that the sum of length of tangent and sub-tangent at any point is proportional to product of coordinates of point of tangency.

Show that in the curve y=a log(x^(2)-a^(2)) the sum the lengths of the tangent and the subtangent at any point varies as the product of the coordinates of the point.

The length of the subtangent at any point on the curve y=be^(x/3) is