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Circle equationsc

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Circle equationsc

by Amrabdelnaby » Mon Dec 14, 2015 4:17 pm
Could you please help me with this?

The standard equation of a circle is (x−h)2+(y−k)2=r2, where the point (h,k) is the center of the circle and r represents the length of the radius. If a particular circle can be represented by the equation x2+y2−8x+2y=−1, what is the radius of that circle?

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by MartyMurray » Mon Dec 14, 2015 9:41 pm
I guess you just have to, by adding some value to both sides, line up the equation so that it fits the circle form.

x² + y² - 8x + 2y = -1

(x² - 8x) + (y² + 2y) = -1

For x² - 8x to work as part of the result of squaring x - h, you need 16 to create x² - 8x + 16, which is (x - 4)².

For y² + 2y to work as part of the result of squaring y - k, you need 1 to create y² + 2y + 1, which is (y - (-1))².

So add 16 and 1 to both sides of the equation to get the following.

(x² - 8x + 16) + (y² + 2y + 1) = 16

So the radius is √16 = 4

The correct answer is D.
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