Find the intercepts if any

Question

x^2+y^2+8x-8y-49=0

Labe

Answer 1

This is a circle

x^2 + 8 x + 16 + y^2 -8y +16 = 49+32 = 81 = 9^2

(x+4)^2 + (y-4)^2 = 9^2

center at x = -4 , y = +4 , radius 9

sketch it

Now do the problem

when x = 0
y^2 - 8 y - 49 = 0
y = [ 8 +/- sqrt (64+196) ]/2
y = 4 (of course) +/- 6.32

when y = 0
x^2 + 8 x - 49 = 0
x = [ -8 +/- sqrt (64+196)]/2
x = -4 +/- 6.32