x^2+y^2+8x-14y+10=9

Question

find the radius, center and intercepts

Answer 1

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)