# Equation of circle

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• Mar 17th 2008, 04:04 PM
Shinjiro
Equation of circle
Find the equation of the circle which passes through (-1, 4)and with center at (4,-8)

I know this is an easy question but I just cant find the formula for how to find the equation. Any help appreciated.
• Mar 17th 2008, 04:08 PM
thegame189
I think you'd find the distance from the center to that point. That's the radius.
• Mar 17th 2008, 04:31 PM
topher0805
The standard form for the equation of a circle is:

$\displaystyle (x - h)^2 + (y - k)^2 = r^2$

Where the point $\displaystyle (h,k)$ is the center of the circle.

We are given that the center is found at (4,-8) so we have our equation so far:

$\displaystyle (x - 4)^2 + (y + 8)^2 = r^2$

Now we just need to find the radius. We have been given one point on the circle, so to find the radius we simply need to find the distance from the center of the circle to that point. Recall the distance formula:

$\displaystyle d = \sqrt {(x_2-x_1)^2+(y_2-y_1)^2}$

Plug your values in to find the radius, then simply enter that into the previous equation to get your final answer. :)
• Mar 17th 2008, 04:36 PM
Shinjiro
Ah. The answer is $\displaystyle (x-4)^2 + (y+8)^2 = 169$ from what you said about the distance from those 2 points.
• Mar 17th 2008, 04:45 PM
topher0805
That is correct.