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.

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.

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 .

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 equation of the curve such that the square of the intercept cut off by any tangent from the y-axis is equal to the product of the co-ordinate of the point of tangency.

The equation of the curve which is such that the portion of the axis of x cut-off between the origin and tangent at any point is proportional to the ordinate of that point is

The equation of the curve which is such that the portion of the axis of x cut off between the origin and tangent at any point is proportional to the ordinate of that point is

A curve y=f(x) passes through point P(1,1). The normal to the curve at P is a (y-1)+(x-1)=0. If the slope of the tangent at any point on the curve is proportional to the ordinate of the point,then the equation of the curve is

A curve y=f(x) passes through the point P(1,1) . The normal to the curve at P is a(y-1)+(x-1)=0 . If the slope of the tangent at any point on the curve is proportional to the ordinate of the point. Determine the equation of the curve. Also obtain the area bounded by the y-axis, the curve and the normal to the curve at P .