AP EAPCET 23-Aug-2021 Shift 1 Paper

Given equation of circle isx2+y2−14x+2y+25=0
⇒(x2−14x+49)+(y2+2y+1) −49−1+25=0
(x−7)2+(y+1)2=25=52 ⇒ Radius of circle =5
Centre of circle =(7,−1)
Distance between origin and centre =√(7)2+(−1)2=√50=5√2
∴OP=5√2 and PA=5
Now, sin‌θ=

AP

OP

=

5

5√2

=

1

√2

⇒θ=45°
Similarly, sin‌α=

PR

OP

=

5

5√2

=

1

√2

⇒α=45°
∴θ+α=90°
Thus, angle between two tangent drawn from origin to given circle is 90°.