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Find the center and radius of the circle:
x2 + y2 - 8x – 12y + 43 = 0

1 Answer

4 votes

Answer:

  • center: (4, 6)
  • radius: 3

Explanation:

You want the center and radius of the circle defined by ...

x² +y² -8x -12y +43 = 0

Completing the square

We can separate the constant term and complete the squares involving the x- and y-terms.

x² +y² -8x -12y = -43

(x² -8x +16) +(y² -12y +36) = -43 +16 +36

(x -4)² +(y -6)² = 9

Parameters

The standard form equation for a circle is ...

(x -h)² +(y -k)² = r² . . . . . . circle with radius r and center (h, k)

Comparing this to the equation we have, we see that ...

(h, k) = (4, 6)

r² = 9 ⇒ r = 3

The center is (4, 6) and the radius is 3.

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Find the center and radius of the circle: x2 + y2 - 8x – 12y + 43 = 0-example-1
User Dastan
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