AP EAMCET Engineering 23 Apr 2019 Shift 1 Paper

The equation of ellipse is

x2

25

+

y2

16

= 1
Let the point P(5‌cos‌θ,4‌sin‌θ) on ellipse then the equation of tangent to ellipse is,
x(

cos‌θ

5

)+y(

sin‌θ

4

)=1 ....(I)
So, the point Q is Q(

5

cos‌θ

,0 ) and point R is R(0,5‌sec‌θ) The equation of the circle with QR as diameter is,
x(x−5‌sec‌θ)+y(y−5‌sec‌θ)=0
x2+y2−(5‌sec‌θ)x−(5‌sec‌θ)y=0
The above circle passes through the origin.