Question

`x^2-6x+y^2-8x=0`

The graph of the given equation in the xy-plane is a circle. What is the radius of the circle? (You may NOT use a calculator!)

A) 2
B) 3
C) 4
D) 5

An explanation along with the answer would be extremely helpful!!! Thank you!

Answer 1

D

Step-by-step explanation:

Start with the general equation of a circle

(x-h)² + (y-k)² = r²

where (h, k) are the coordinates of the center, and r is the radius

x²-6x+y²-8y = 0 , form prefect squares while keeping the equation balanced

x²-6x +3² +y²-8y +4² = 3² + 4²

(x-3)² +(y-4)² = 9 + 16

(x-3)² +(y-4)² = 25

(x-3)² +(y-4)² = 5² , compare with (x-h)² + (y-k)² = r²

Radius = 5