Question

find the center and the radius of the circle
$x {}^{2} + y {}^{2} + 8x + 10y - 8 = 0$
​

Answer 1

Answer:

cenre = (-4,-5)

radius = 7units

Step-by-step explanation:

$x^2+ y^2 + 8x + 10y -8 = 0$

Given equation is of the form $x^2+ y^2 + 2gx + 2fy + c$ = 0,

where(-g,-f) is the centre of the circle

on comparing, 2g = 8   => g=8/2  => g = 4 units

                     & 2f = 10   => f=10/2  => f = 5 units

=> centre is (-g,-f) => (-4,-5)

we know that radius , r = $\sqrt{(g^2+f^2-c )}$ units

                                       = $\sqrt{(-4)^2+(-5)^2-(-8) }$ units

                                       = $\sqrt{16+25+8 }$ units

                                       = $\sqrt{49 }$ units

                                       = 7 units