x^2+y^2+8x-14y+10=9 find the radius, center and intercepts
x^2+y^2+8x-14y+10=9 rearrange slightly.
x^2 + 8x + y^2 – 14y = -1 now complete the squares.
(x^2 + 8x + 16) – 16 + (y^2 – 14y + 49) – 49 = -1 simplify.
(x + 4)^2 + (y – 7)^2 = -1 + 49 + 16
(x + 4)^2 + (y – 7)^2 = 64
(x + 4)^2 + (y – 7)^2 = 8^2
The above is the equation of circle centre = (-4, 7), and radius = 8.
y-intercepts (x = 0)
(4)^2 + (y – 7)^2 = 8^2
(y – 7)^2 = 64 – 16 = 48
y = 7 +/- 4.sqrt(3)
x-intercepts (y = 0)
(x + 4)^2 + (-7)^2 = 8^2
(x + 4)^2 = 64 – 49 = 15
x = -4 +/- sqrt(15)