Find the curve for which area of triangle formed by x-axis, tangent drawn at any point on the curve and radius vector of point of tangency is constant, equal to `a^2`

A curve has the property that area of triangle formed by the x-axis, the tangent to the curve and radius vector of the point of tangency is k^(2) . The equation of all such curves passing through (0, 1) is ln (ay) = (xy^(b))/(2k^(2)) then

The area of the triangle formed by the tangent to the curve xy=a^(2) at any point on the curve with the coordinate axis is

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.

The area of triangle formed by tangent and normal at point (sqrt(3),1) of the curve x^(2)+y^(2)=4 and x -axis is :

If the least area of triangle formed by tangent,normal at any point P on the curve y=f(x) and X -axis is 4sq. unit.Then the ordinate of the point P(P lies in first quadrant) is

The equation of the curve,passing through (2, 5) and having the area of triangle formed by the X-axis,the ordinate of a point on the curve and the tangent at the point 5 sq.units as

A curve in the first quadrant is such that the area of the triangle formed in the first quadrant bythe X-axis,a tangent to the curve at any of its point P and radius vector of the point P is 2 sq .units.If the curve passes through (2,1), find the equation of the curve.

" The area of the triangle formed by the tangent and normal at "(a,a)" on the curve "y(2a-x)=x^(2)" and the "x" -axis is "