If a point P x , y moves along the ellipse x 2 25 + y 2 16 = 1 and if C is the centre of the ellipse, then the sum of maximum and minimum values of C P is

Step-by-step solution

Given equation of ellipse is x 2 25 + y 2 16 = 1 . Here a = 5 ,   b = 4 and the centre of the ellipse is ( 0 , 0 ) . The major axis of ellipse is along the X - axis and minor axis is along Y - axis. The distance of point P ( x , y ) from the centre of the ellipse C is maximum, only when the point P ( x , y ) is on the endpoint of major axis (or at the vertex of ellipse along the major-axis). Therefore, coordinate of point P at the endpoint of major-axis is ( 5 , 0 ) or ( - 5 , 0 ) . Hence, maximum value of C P