Question

Write the equation of the circle with center (-6, -4) and containing the point (-2, -1).

Answer 1

you can easily calculate the radius, you have the center and one point, so use the distance formula.

Answer 2

Ok thanks, after that, Im not so sure what to do

Answer 3

Sorry, I am back

the general formula of a circle is

\[ f(x,y)=(x-u)^2 + (y-v)^2 = r^2 \] where (u,v) are the x,y respective coordinates of the center and r is the radius.

Answer 4

so it would be (-2+6)^2+(-1+4)=7.4^2

Answer 5

hmm well, you have to calculate the radius first and then substitute the center, so you get

\[ f(x,y)=(x+6)^2+(y+4)^2=25 \]

Answer 6

the radius is 5, you can get that with the distance formula, or by substituting all the points in the given formula above.

Answer 7

Okay, so I did it right the first time

Answer 8

the end product is that I got 25=25

Answer 9

but how would I write that in the correct form?

Answer 10

(4)^2+(3)^2=25 ?

Answer 11

no, see, the given equation, I have already posted it above, describes a circle. the only thing you need to describe a circle is the radius and the points of the origin

Answer 12

origin= origin of the circle, it's center. Just not to confuse you

Answer 13

So in this case, the radius is 5, for the formula you need r^5 = 25. The Center is given by the points (u,v) = (-6,-4). Only substitute these into the general formula for a circle and you will get:

\[ f(x,y)= (x+6)^2(y+4)^2=25 \]

http://www.wolframalpha.com/input/?i=+graph+%28x%2B6%29%5E2%2B%28y%2B4%29%5E2%3D25 here is the graph

Answer 14

so im just overthinking it, that it.