The family of curves whose x and y intercepts of a tangent at any point are respectively double the x and y coordinates of that point is

Step-by-step solution

Let the point on the curve be (h, k) . According to the question, the equation of the tangent will be x 2 h + y 2 k =1 y 2 k =1- y 2 h y=- ( 2 k 2 h ) x+2 k So, the slope of tangent will be (- k h ) . Now, d y d x =- h k =- y x d y y =- d x x On integrating both sides, we get d y d y =- d x x y=- x+ C y= C x y= C x x y=C