Question

What is the general form of the equation of a circle with center at (a, b) and radius of length m?

A)x^2 + y^2 - 2ax - 2by + (a^2 + b^2 - m^2) = 0

B)x^2 + y^2 + 2ax + 2by + (a2 + b^2 - m^2) = 0

C)x^2 + y^2 - 2ax - 2by + (a + b - m^2) = 0

D)x^2 + y^2 + 2ax + 2by + a^2 + b^2 = -m^2

Answer 1

all you need to do for this is take the more familiar form

(x-a)^2 + (y-b)^2 = m^2

expand the brackets as follows
(x-a)(x-a)=?
(y-b)(y-b) =

then rearrange the equation so it looks like one of your answers

Answer 2

ok so how would i do that?

Answer 3

I have given you the mains steps already.

in th efirst equation you have (x-a)^2

That is the same as (x-a)(x-a)

First write what that multiplies out to (use FOIL?)

Answer 4

okay so
(x-a)^2 + (y-b)^2 = m^2
is the same as
x^2-2ax+a^2 + y^2-2by+b^2-m^2 = 0
right? so the answer would be A?

Answer 5

Well done - that's correct.