Q92 / 160 · AP EAMCET 2021 (20 Aug Shift 2) · Mathematics

The centre and radius of the circle $x^{2} + y^{2} + 8 x + 10 y - 8 = 0$ respectively are

Solution

Given that: $x^{2} + y^{2} + 8 x + 10 y - 8 = 0$

As we know that $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$

has centre $(- g, - f)$ and $r = \sqrt{g^{2} + f^{2} - c}$

here, $g = 4, f = 5, c = - 8$

centre $\equiv (- 4, - 5),$

radius = r = $\sqrt{16 + 25 + 8} = 7$

Hence, the correct answer is option: 'A'.