Question

**PLEASE HELP ASAP** Terri is analyzing a circle, y^2 + x^2 = 36, and a linear function g(x). Will they intersect?

Answer 1

We analyze the linear function to find that it has equation $y=x$.  Drawing the line, we find that it will intersect the circle at negative and positive x-coordinates.

We can prove this by substituting $y=x$ into the given equation:

$x^2+x^2=36$

$2x^2=36$

$x^2 = 18$

$x = \pm 3\sqrt{2}$

Hence, $x = 3\sqrt{2}$ or $-\sqrt{2}$, so there are both positive and negative values for $x$.