Find the equation in standard form of a circle that satisfies the given condition.?

Question

Center C = (-5,1), passing through (3,1)

Answer 1

radius = (3--5)=8
therefore (x--5)^2 + (y-1)^2 = 8^2
therefore (x+5)^2 + (y-1)^2 = 64

Answer 2

The formula of a circle is as follows:

(x - h)^2 + (y - k)^2 = r^2, where (h,k) is the coordinates of the center, and r is the radius. So we have

(x - (-5))^2 + (y - 1)^2 = r^2
(x + 5)^2 + (y - 1)^2 = r^2

But we know that it passes through (3,1), so we plug in those values for x and y to solve for r.

(3 + 5)^2 + (1 - 1)^2 = r^2
8^2 + 0 = r^2
64 = r^2
Remember that we really want to solve for r^2 and not necessarily r, so we're happy with r^2 = 64.

As a summary, we first wrote down the formula of a general circle:

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

And then we plugged in the values for the center of the circle

(x + 5)^2 + (y - 1)^2 = r^2

And then we solved for r^2, which was 64

(x + 5)^2 + (y - 1)^2 = 64

And that's your equation.