Acircle is centered at (5. -9) and has a radius of 12. which of the following is the equation for this circle?
(x - 5)2 + (y + 9)2 = 12
(x - 5)2 + (y + 9)2 = 144
(x + 5)2 + (- 9)2 = 144
(x + 5)2 + (- 9)2 = 12

(x - 5)² + (y + 9)² = 144

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (5, - 9) and r = 12, thus

(x - 5)² + (y - (- 9))² = 12², that is

(x - 5)² + (y + 9)² = 144

B.) (X - 5)2 + (y + 9)2 = 144

Step-by-step explanation:

For this question, it gives us the (h, k) values, (5, -9) and the radius, 12. To find the correct equation, we just need to plug in the values. The question does not ask for (x, y) so we do not need to worry about that. An interesting point to note is that the equation in its original form uses negative signs: (x - h)2 + (y - k)2 = r2. So this would greatly impact what our numbers would be. The h value 5 would become -5 and the k value -9 would become 9. About the radius, options A and D are incorrect. In the original equation, the result looks like "r2". The 12 is not squared in options A and D. And because option C did not change the signs, it would be incorrect as well. That leaves us with option B.

Hope this helps :)

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