Conic Sections Question 2

A circle with equation $x^2+y^2=144$ is graphed in the standard $(x,y)$ coordinate plane. At what points does the circle intersect the $x$ -axis?

(-6,0)

and

(6,0)

(-12,0)

and

(12,0)

(-24,0)

and

(24,0)

(-72,0)

and

(72,0)

(-144,0)

and

(144,0)

Approach 1

The equation of a circle:

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

This circle has a center at $(0,0)$ and a radius of 12. We can go 12 to the left and to the right to get the $x$ -intercepts.

Approach 2

x^2+y^2=144

x^2 +(0)^2=144

x^2 = 144

x =\pm \sqrt{144}

x=\pm 12