A circle has the equation (x−4)2+(y−1)2=34. What are the coordinates of the center and the length of the radius?

Answer 1

Hi Jackson,

Remember that our standard equation for a circle at the origin (0,0) is x² + y² = r².

The equation (x - h)² + (y - k)² = r² is for a circle at the origin (h, k).

(x-4)² + (y-1)² = 34

So, we can tell from the form of the equation that our origin is (4, 1) and our radius is √34.

Answer 2

Divide by 2 to get

(x-4)^2 + (y-1)^2 = 17 = (sqr17)^2

center is (4,1) with radius = sqr17