Question

A circle in the xyxyx, y-plane has its center at the point (-6,1)(−6,1)(, minus, 6, comma, 1, ). If the point (7,12)(7,12)(, 7, comma, 12, )lies on the circle, what is the radius of the circle? Round the answer to the nearest tenth.

Answer 1

Answer:

r=17.0

Step-by-step explanation:

In a circle with center (h,k) and any point (x,y) on the circle, the radius of the circle is given as:

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

Center (h,k)=(-6,1)

(x,y)=(7,12)

$r^2=(x -h)^2 + (y - k)^2 \\r^2=(7 -(-6))^2 + (12 - 1)^2\\r^2=(7 +6)^2 + 11^2\\r^2=13^2 + 11^2=169+121=290\\r=\sqrt{290}=17.03$

radius, r=17.0 (to the nearest tenth)