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

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 equation of the curve which is such that the area of the rectangle constructed on the abscissa of any point and the intercept of the tangent at this point on the y-axis is equal to 4.

For the curve x y=c , prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.

For the curve x y=c , prove that the portion of the tangent intercepted between the coordinate axes is bisected at the point of contact.

The distance between the origin and the tangent to the curve y=e^(2x)+x^2 drawn at the point x=0 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

Find the equation of the curve passing through the point (0,1), if the slope of the tangent to the curve at any point (x,y), is equal to the sum of x coordinate and product of x coordinate and y coordinate of that point.

Find the equation of a curve passing through the origin, given that the slope of the tangent of the curve at any point (x,y) is equal to tha sum of the coordinates of the point.

What are X co-ordinates of each point on Y-axis?

Find the equation of the curve passing through the point (2,-3), given that the slope of the tangent to the curve at any point (x,y) is (2x)/(y^(2))