A circle has a center at (−4, −5) and a radius of √6. What is the equation of the circle?
A. (x − 4)² + (y − 5)² = √6
B. (x + 4)² + (y + 5)² = √6
C. (x − 4)² + (y − 5)² = 6
D. (x + 4)² + (y + 5)² = 6
A circle has a center at (−4, −5) and a radius of √6. What is the equation of the circle?
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The correct answer is D. (x + 4)² + (y + 5)² = 6.
To find the equation of a circle with a given center and radius, we use the standard form of the equation:
[
(x – h)² + (y – k)² = r²
]
where ((h, k)) is the center of the circle and (r) is the radius.
In this case, the center is ((-4, -5)) and the radius is (sqrt{6}).
1. Substitute (h = -4) and (k = -5):
[
(x + 4)² + (y + 5)²
]
2. Next, square the radius (sqrt{6}):
[
(sqrt{6})² = 6
]
3. Combine the results:
[
(x + 4)² + (y + 5)² = 6
]
Thus, the equation of the circle is ((x + 4)² + (y + 5)² = 6), which matches option D.