Question

What is the standard form of the equation of a circle that has its center at (-2, -3) and passes through the point (-2, 0)?

Answer 1

(A) (x + 2)^2 + (y + 3)^2 = 9
(B) (x − 2)^2 + (y − 3)^2 = 16
(C) (x − 2)^2 + (y − 3)^2 = 4
(D) (x + 2)^2 + (y + 3)^2 = 16
(E) (x − 2)^2 + (y + 3)^2 = 9

Answer 2

formula for a circle with radius \(r\) and center at \((h,k)\) is \[(x-h)^2 + (y-k)^2 = r^2\]You don't know \(r\) yet, but you do know the center. What is the first pass at the formula going to be?

Answer 3

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

Answer 4

Yes. Can you simplify that any more?

by the way, you need some more parentheses — \((x-(-2))^2 + (y-(-3))^2 = r^2\)

Next step is to find the value of \(r\). There are two ways that come to mind how you could do this.

1) find the length of the radius from \((-2,-3)\) to \((-2,0)\) with the distance formula \[d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\]which gives the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\)

2) just plug in your known point \((-2,0)\) as \((x,y)\) in the formula and find the value of \(r\)

Answer 5

Personally, I think the second one is easier. You'll actually end up with the value of \(r^2\), and that's what you want to use in the formula, so no need to solve it for \(r\)

Answer 6

(x+2)^2 + (y+3)^2=r^2 Does it simplify to this?

Answer 7

Yes, good job not getting tripped up by the - signs in the formula.

Answer 8

Ok now do i raise (x+2),(y+3) by the power of 2?

Answer 9

Thank you @whpalmer4 turns out i didn't have to do this problem. Although i have one pretty similar, would you mind?

Answer 10

(x + 5.5)2 + (y + 4)2 = 3.5 , (x − 5.5)2 + (y − 4)2 = 3.5 I know the answer is between these two because the center is at (5.5,4), and the radius is 3.5.

Answer 11

Don't get tripped by the negative sign in the formula!

Answer 12

Do you recall the formula?

Answer 13

For the equation of a line?

Answer 14

Of a circle.

Answer 15

Duh, sorry haha.

Answer 16

(x-a)2 + (y-b)2 = r2 ?

Answer 17

Yep, what's a, b, and r?

Answer 18

a=5.5, b=4, c=1.75 ?

Answer 19

wait no.

Answer 20

Why 1.75?

Answer 21

3.5* I divided by 2 for some reason.

Answer 22

Now plug in the values?

Answer 23

(x-5.5)^2+(y-4)^2=3.5^2

Answer 24

Thank you @kc_kennylau

Answer 25

I appreciate it!!