Question

ans this PLZ HURRY class 11 math, circle question.!!

Answer 1

we have a circle
${x}^{2} + {y}^{2} + 2x + 2y - 23 = 0 \\ centre = ( - 1.. - 1)$
centre=(-1,-1)
let the line perpendicular to x-y+8=0 be x-y+c=0
since (-1,-1) lies on it hence will satisfy
$- x - y + c = 0 \\ - ( - 1) - ( - 1) + c = 0 \\ c = - 2\\ therefore \: line \: is \: \\ x - y - 2 = 0 \\ x - y = 2$
mark as brainliest if helped

Answer 2

centre of circle eqn is given as
centre=(-g,-f) for x^2 + y^2 +2gx+2fy+c=0
here centre is (-1,-1)
then...for that line
slope=-a/b = -1/-1 = 1
given ...line is perpendicular so slope becomes -1
eqn of straight line is
y-y1 = slope ×(x-x1)
y+1= -1 (x+1)
y+1=-x-1
x+y+2=0
is final equation
pls mark as as brainiest if it is correct