Question

Help! Hurry! NO SPAM!!!! I will mark brainliest if you get it correct, and show your work. Identify the equation for the circle with center (3, 7) that contains the point (9, 11).

Answer 1

First we compute the distance between the center and the given point which is exactly the radius

r =

$\sqrt{(x2 - x1) + (y2 - y1)} = \sqrt{9 - 3 + 11 - 7} = \sqrt{10}$

Now that we know the center and the radius, we can write the equation of a circle with given radius and center:

${(x - h)}^{2} + {(y - k)}^{2} = {r}^{2}$

where (h,k) represent the coordinates of the center (3,7).

We substitute and obtain

${(x - 3)}^{2} + {(y - 7)}^{2} = { \sqrt{10} }^{2} \\ {(x - 3)}^{2} + {(y - 7)}^{2} = 10 \\ {x}^{2} - 6x + 9 + {y}^{2} - 14y + 49 = 10 \\ {x}^{2} + {y}^{2} - 6x - 14y + 48 = 0$