College Math CLEP Prep Practice Exam

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What equation describes a circle with its center at (3,4) and a radius of 5?

x^2+y^2=25
x^2+(y-4)^2=25
(x-3)^2+(y-4)^2=25
(x+3)^2+(y+4)^2=25

The correct answer is: (x-3)^2+(y-4)^2=25

This is because the center of the circle is given as (3,4) in the question, so we know that (h,k)=(3,4). The equation for a circle with center (h,k) and radius r is (x-h)^2+(y-k)^2=r^2. So to find the equation for this circle, we plug in our values of h=3, k=4, and r=5. This gives us (x-3)^2+(y-4)^2=25, which matches the equation given in choice C. Therefore, option C is the correct answer. Option A is incorrect because it does not take into account the center of the circle, which is given as (3,4). Option B is incorrect because it incorrectly changes the center of the circle. Finally, option D is incorrect because it incorrectly adds constants to the values