Question

The graph of the equation LaTeX: x^2+y^2-20x+14y+28=0

x
2
+
y
2
−
20
x
+
14
y
+
28
=
0
is a circle. What is the radius of this circle?
Group of answer choices

Answer 1

radius = 11

Explanation:

The equation of a circle in general form is

x² + y² + 2gx + 2fy + c = 0

with radius =
`√(g^2+f^2-c)`

x² + y² - 20x + 14y + 28 = 0 ← is in general form

with 2g = - 20 ⇒ g = - 10

2f = 14 ⇒ f = 7 and c = 28, thus

radius =
`√((-10)^2+7^2-28)` =
`√(100+49-28)` =
`√(121)` = 11