Question

what is the equation of the circle with center (2, –5) that passes through the point (–2, 10)?

Answer 1

general equation of a circle:

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

where the circle's center is the point (h, k) and the radius has length r

Answer 2

okay

Answer 3

if the circle passes through (-2, 10), it means that the radius is the distance between the center and that point.

\[d = r = \sqrt{(x_2 - x_1)^{2} + (y_2 - y_1)^{2}}\]

Answer 4

d meaning distance for the standard distance formula above (not to be confused with diameter)

Answer 5

So what should I do, I don't understand. I follow what your writing but I don't know how to solve.

Answer 6

you simply plug in. lets call the center (x1,y1) and the point (x2,y2)

Answer 7

so (x1,y1) is (2,-5) and then (x2,y2) is (-2,10). Then what do I do?

Answer 8

yes, you'd find r:

r = \[r = \sqrt{(-2 - 2)^{2} + (10 - (-5))^{2}} = \sqrt{16 + 225}\]

then you have h, k and r for the general equation formula. where (h,k) = (x1,y1) = center of circle

\[(x - 2)^{2} + (y - (-5))^{2} = (\sqrt{16+225})^{2}\]

simplifying will give the final answer; the equation of the circle

Answer 9

I am stuck...

Answer 10

I don't know how to simplify that..

Answer 11

simplified version would be:

\[(x - 2)^{2} + (y + 5)^{2} = 241\]

Answer 12

I am in all seriousness don't know how. I am not trying to just get the answer. I want to know how to do it.

Answer 13

i believe :). i didn't suspect you of trying to just get the answer lol

Answer 14

How is that the answer it's not a choice do I have to do something else

Answer 15

I was just wanting to make sure you knew.

Answer 16

what are your answer choices?

Answer 17

Are \(x^2+y^2-4x+10y+29=241\) or \(x^2+y^2-4x+10y=212\) among your answer choices? That's what you would get if you expanded the answer.

Answer 18

Though normally one would keep it in the form given by Euler271, as it is easy to then see the properties of the circle without laboriously graphing it.