Let E be an ellipse whose major axis is X -axis and minor axis is Y -axis. If the distance of a point ( 5 2 , 2 3 ) on E from its foci are 7 2 and 13 2 , then the eccentricity of the ellipse E is

Step-by-step solution

Let the point ( 5 2 , 2 3 ) be P Then, S P+S P=2 a 7 2 + 13 2 =2 a a=5 The focus of the ellipse are ( a e, 0) ( 5 e, 0) aligned & SP = (5 e- 5 2 )^2+(2 3 -0)^2 & ( 7 2 )^2= (5 e- 5 2 )^2+12 & 49 4 -12= (5 e- 5 2 )^2 6 4 (5 e- 5 2 )^2 & 5 e- 5 2 = 1 2 5 e=3 e= 3 5 aligned