A circle is represented by the equation below:(x + 8)2 + (y − 3)2 = 100Which statement is true?Group of answer choicesThe circle is centered at (−8, 3) and has a radius of 20.The circle is centered at (8, −3) and has a diameter of 20.The circle is centered at (8, −3) and has a radius of 20.The circle is centered at (−8, 3) and has a diameter of 20.
Question
A circle is represented by the equation below:(x + 8)2 + (y − 3)2 = 100Which statement is true?Group of answer choicesThe circle is centered at (−8, 3) and has a radius of 20.The circle is centered at (8, −3) and has a diameter of 20.The circle is centered at (8, −3) and has a radius of 20.The circle is centered at (−8, 3) and has a diameter of 20.
Solution 1
The circle is centered at (−8, 3) and has a radius of 10.
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.
Comparing this with the given equation (x + 8)² + (y - 3)² = 100, we can see that h = -8, k = 3, and r² = 100. Therefore, the center of the circle is (-8, 3) and the radius is the square root of 100, which is 10.
None of the provided answer choices exactly match this, but the closest one would be "The circle is centered at (−8, 3) and has a radius of 20." However, the radius should be 10, not 20.
Solution 2
The circle is centered at (−8, 3) and has a radius of 10.
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 + 8)² + (y - 3)² = 100, you can see that h = -8 and k = 3. So, the center of the circle is (-8, 3).
The right side of the equation, 100, is r². So, r² = 100. Taking the square root of both sides gives r = 10.
Therefore, the circle is centered at (-8, 3) and has a radius of 10. None of the provided answer choices are correct.
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