Question

Using the following equation, find the center and radius of the circle. You must show all work and calculations to receive credit.

x2 −2x + y2 − 6y = 26

Answer 1

[(x^2 - 2x + 1) + (y^2 - 6x + 9) = 26 + 1 + 9\]
now you need to complete factor both quadratics

\[(x - 1)^2 + (x - 3)^2 = 6^2\]

so the general form is

\[(x - h)^2 + (y - k)^2 = r^2\]

so the centre is (h, k) and radius is r

you need to match this to your factored equation to find the center and radius

if you match

\[(x -h)^2 + (y - k)^2 = r^2 ...with...(x - 1)^2 + (y - 3)^2 = 6^2\]

h = 1, k = 3 so the center is (1, 3) and the radius is 6