Write the equation of the circle centered at (−6,8)(-6,8) with radius 5252 .
Question
Write the equation of the circle centered at (−6,8)(-6,8) with radius 5252 .
Solution
The general equation of a circle is given by (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.
Given the center of the circle as (-6, 8) and radius as 52, we can substitute these values into the equation.
So, the equation of the circle is:
(x - (-6))² + (y - 8)² = 52²
Simplifying this gives:
(x + 6)² + (y - 8)² = 2704
So, the equation of the circle centered at (-6, 8) with radius 52 is (x + 6)² + (y - 8)² = 2704.
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