Question

A circle has its center at (-2, -3) and a radius of 3 units. What is the equation of the circle?

options:
x + 2)2 + (y + 3)2= 9

(x + 2)2 + (y - 3)2= 9

(x - 2)2 + (y - 3)2 = 3

(x + 2)2 + (y + 3)2 = 3

Answer 1

The equation for a circle is (x-h)^2 + (y-k)^2 = r^2. H is the x-coordinate of the center and k is the y-coordinate of the center. Also, the minus signs I put in the formula HAVE to be minus signs. This means that if I have something like (x-2)^2, this means that the 2 is actually a positive 2. And if I had something like (x+2)^2, this means I actually have a -2 because (x-(-2))^2 = (x+2). Basically, a negative x-coordinate for your center is put in as (x+__)^2 + (y+__)^2 and aminus sign is placed there for the positive values at the center. As for the r^2, it just means to take the given radius and square it. Long explanation. so hope that makes some sense for knowing what to plug in.

Answer 2

ok so i plug in -2 for h and -3 for k
so it would be (x-(-2))2+ (y-(-3))

Answer 3

Exactly. Which would give you (x+2)^2 + (y+3)^2 = r^2. Now just square your radius and youre done.

Answer 4

but isn't the radius 3?

Answer 5

ohh ok i got it

Answer 6

its A right?

Answer 7

It is. But the equation for a circle requires it to be radius squared. The reason it has to be r^2 is because the equation of a circle is actually a mutated form of pythagorean theorem. If you remember the pythagorean theorem, a^2 + b^2 = c^2, this is the SAME thing. So that's why its r^2 = 9 and not just r = 3. SO yes, A, lol.

Answer 8

thanks :)
that helped a lot

Answer 9

Awesome, glad it did ^_^