Write the equation of the circle centered at (−7,10)(-7,10) with radius 8. Fully simplify the equation.
Question
Write the equation of the circle centered at (−7,10) with radius 8. Fully simplify the equation.
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 that the center of the circle is (-7, 10) and the radius is 8, we can substitute these values into the equation to get:
(x - (-7))² + (y - 10)² = 8²
Simplifying this gives:
(x + 7)² + (y - 10)² = 64
This is the equation of the circle.
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