Question

Calculate the radius of a circle by completing the square of the equation x2+y2−16x−10y+40=0
𝑥
2
+
𝑦
2
−
16
𝑥
−
10
𝑦
+
40
=
0
.(1 point)
radius =
=

Answer 1

Complete the square:

x^2 − 16x = (x − 8)^2 − 64
y^2 − 10y = (y − 5)^2 − 25

Substitute into the equation:
(x − 8)^2 − 64 + (y − 5)^2 − 25 + 40 = 0
⇒ (x − 8)^2 + (y − 5)^2 − 49 = 0
⇒ (x − 8)^2 + (y − 5)^2 = 49

Thus radius = sqrt(49) = 7.