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=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.

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.

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.

If the length of the sub-tangent at any point to the curve xy^(n)=a is proportional to the abscissa,then n is

Show that equation to the curve such that the y-intercept cut off by the tangent at an arbitrary point is proportional to the square of the ordinate of the point of tangency is of the form a/x+b/y=1 .

Show that equation to the curve such that the y-intercept cut off by the tangent at an arbitrary point is proportional to the square of the ordinate of the point of tangency is of the form a/x+b/y=1 .

Show that equation to the curve such that the y-intercept cut off by the tangent at an arbitrary point is proportional to the square of the ordinate of the point of tangency is of the form a/x+b/y=1 .

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.

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.

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.