Which of the following equations correctly represents a circle centered at the origin with a radius of 5?A.(x - 5)2 + y2 = 25B.(x - 5)2 + (y - 5)2 = 5C.x2 + y2 = 5D.x2 + y2 = 25SUBMITarrow_backPREVIOUS
Question
Which of the following equations correctly represents a circle centered at the origin with a radius of 5?A.(x - 5)2 + y2 = 25B.(x - 5)2 + (y - 5)2 = 5C.x2 + y2 = 5D.x2 + y2 = 25SUBMITarrow_backPREVIOUS
Solution
The equation of a circle centered at the origin (0,0) with radius r is given by the formula x² + y² = r².
Given that the radius of the circle is 5, we substitute r = 5 into the formula to get:
x² + y² = 5²
Simplifying the right side of the equation gives:
x² + y² = 25
Therefore, the correct equation that represents a circle centered at the origin with a radius of 5 is D. x² + y² = 25.
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