Question

Find the center and the radius of the circle whose equation is x square -16x+y square = 36

Answer 1

center: (8, 0)

radius: 10

Explanation:

The equation of a circle in a standard form:

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

(h, k) - center

r - radius

We have the equation:

`x^2-16x+y^2=36\\\\x^2-2(x)(8)+y^2=36\qquad\text{add}\ 8^2\ \text{to both sides}\\\\\underbrace{x^2-2(x)(8)+8^2}_((*))+y^2=36+8^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\qquad(*)\\\\(x-8)^2+(y-0)^2=36+64\\\\(x-8)^2+(y-0)^2=100\\\\(x-8)^2+(y-0)^2=10^2\\\\\text{Therefore}\\\\center:(8,\ 0)\\radius:10`