TS EAMCET 19-July-2022 Shift 1 Solved Paper

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.