A circle is represented by the equation below:(x + 2)2 + (y − 4)2 = 225Which statement is true? (5 points)Group of answer choicesThe circle is centered at (−2, 4) and has a radius of 15.The circle is centered at (2, −4) and has a diameter of 15.The circle is centered at (2, −4) and has a radius of 15.The circle is centered at (−2, 4) and has a diameter of 15.
Question
A circle is represented by the equation below:(x + 2)2 + (y − 4)2 = 225Which statement is true? (5 points)Group of answer choicesThe circle is centered at (−2, 4) and has a radius of 15.The circle is centered at (2, −4) and has a diameter of 15.The circle is centered at (2, −4) and has a radius of 15.The circle is centered at (−2, 4) and has a diameter of 15.
Solution
The circle is centered at (−2, 4) and has a radius of 15.
Here's why:
The general equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.
In the given equation, (x + 2)² + (y - 4)² = 225, you can see that h = -2 and k = 4, so the center of the circle is (-2, 4).
The radius r is the square root of the number on the right side of the equation, so r = sqrt(225) = 15.
Therefore, the circle is centered at (-2, 4) and has a radius of 15.
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