Question

Which equation describes the circle having center point (3,5) and radius r = 2

in standard form?

Answer 1

x^2 + y^2 - 6x - 10y + 30 = 0.

Explanation:

In factor form the general equation is:

(x - h)^2 + (y - k)^2 = r^2 where (h, k) is the centre and r = the radius.

So here we have:

(x - 3)^2 + (y - 5)^2 = 4.

Converting to Standard Form:

= x^2 - 6x + 9 + y^2 - 10y + 25 = 4

x^2 + y^2 - 6x - 10y + 9 + 25 - 4 = 0

x^2 + y^2 - 6x - 10y + 30 = 0.