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belka [17]
4 years ago
9

an equation of a circle is x2 + y2 + 10x – 6y + 18 = 0. . . . A.Show all your work in determining the center and radius of this

circle. . . B.In complete sentences, explain the procedure used.
Mathematics
1 answer:
MariettaO [177]4 years ago
7 0

A circle is a set of points in a plane equidistant from a fixed point. It has a general formula of x² + y² = r². This is if the center is at the origin. However, if the center at point h and k, the equation becomes (x-h)² + (y-k)² = r².<span>

We write the given equation in the form (x-h)² + (y-k)² = r² by completing the square.
</span>

<span>x</span>²<span> + y</span>²<span> + 10x – 6y + 18 = 0</span>

<span> (x² + 10x + 25 )+ (y² - 6y + 9) = −18 + 25 + 9 = 16
(x + 5)² + (y + 3)² = (4)²

Therefore,

center = (-5, -5)
radius = 4</span>

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