Question

Write the equation in standard form for the circle passing through (2,6) centered at the origin.

Answer 1

Answer:  x^2 + y^2 = 40

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Explanation:

The center is the origin, so (h,k) = (0,0).

The point (x,y) = (2,6) is on the circle's edge. We'll use these four values to find the value of r^2

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

(2-0)^2 + (6-0)^2 = r^2

2^2 + 6^2 = r^2

4 + 36 = r^2

40 = r^2

r^2 = 40

We don't need to solve for r itself. If you wanted to, you'd get the radius to be r = sqrt(40) = 2*sqrt(10) = 6.324555 approximately.

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Since h = 0, k = 0, and r^2 = 40, we can say:

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

(x-0)^2 + (y-0)^2 = 40

x^2 + y^2 = 40