Question

Given the equation x^2 +y^2+8y-65=0
(a) Write the equation in standard form.
(b) State the center, radius, and intercepts.
(c) Submit the graph

Answer 1

(a)
to write this in standard form, you use completing the square for both variables x and y.
x^2 + y^2 + 8y - 65 = 0
x^2 + (y^2 + 8y + 16) - 65 - 16 = 0
x^2 + (y + 4)^2 - 81 = 0
x^2 + (y + 4)^2 = 81
x^2 + (y + 4)^2 = 9^2

(b)
Center: C(0, -4)
Radius = 9
to get intercepts,
x-intercept: let y=0 and solve for x
y-intercept: let x=0 and solve for y

(c)
with center and radius known, you can graph this on a graphing paper. use a compass to draw the circle.

hope this helps~ :)