Assertion vertex of the parabola is (0,0). Here a2=25,b2=16 The image of ellipse
x2
25
+
y2
16
=1 with respect to line x+y=10 is
(x−h)2
16
+
(y−k)2
25
=1......(i) The mid-point of centres of both ellipse must lie on line x+y=10 ⇒
h+k
2
=10 ⇒h+k=20 .......(ii) Slope of the line joining the centres =k∕h Slope of the given line =−1 ∴ The line joining the centres and the given line is perpendicular
k
h
(−1)=−1⇒h=k h+h=20 ( ∵ from Eq. (ii)) 2h=20 ⇒h=10 From Eq. (i),
(x−10)2
16
+
(y−10)2
25
=1 Hence, Assertion and Reason both are true and Reason is the correct explanation of Assertion.