Question

Write the equation of the circle with center (-4, 11) and containing the point (5, -1)

Answer 1

I got a weird answer and I would like to know if it's right.

Answer 2

We can write the equation of a circle if we have the center and the radius. We have the center, but not the radius. So how can we find the radius? Remember that the radius is the same anywhere on the circle. Since the have the point (5,-1) on the circle, we can find the radius by finding the distance between (5,-1) and the center (-4,11). Do you know the distance formula?

Answer 3

Yes I know the distance formula

Answer 4

Ok, so apply the distance formula to those two points. The result will be the radius.

Answer 5

And when you square the answer, the final answer is 15 correct?

Answer 6

I mean find the square root

Answer 7

I got 15 as the radius, is that what you got?

Answer 8

Yes sir

Answer 9

Ok, so you know the standard equation for a circle? We have all the info we need to plug in and get the equation now.

Answer 10

Yes I do know the standard equation of a circle

Answer 11

Ok, so plug in and what do you get?

Answer 12

The equation I got is as follows: (x+4)^2+(y-11)^2-225

Answer 13

Yes, thats what I got as well, but there should be an equal sign right before the 225:
(x+4)^2 + (y-11)^2 = 225

Answer 14

you don't need to complicate this

the general form for a centre at (h, k) is

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

substitute h = -4 and k = 11

which gives

\[(x + 4)^2 + (y - 11)^2 = r^2\]

then just substitute x = 5 and y = -1 to find r^2 and give the equation.

substituting the point into the circle equation is actually using the distance formula.

no need to do it seperately

Answer 15

Oops I meant to put an equal sign there

Answer 16

You could do that as well. Mechanically they're basically doing the same thing.

Answer 17

I appreciate your help

Answer 18

You're welcome, glad I could help

Answer 19

Me too haha