Question

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

Yes, at positive x-coordinates or zero
Yes, at negative x-coordinates or zero
Yes, at negative and positive x-coordinates or zero
No, they will not intersect

Answer 1

will intersect the circle at negative and positive x-coordinates.

Explanation:

^^

Answer 2

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√(2)`

Hence,
`x = 3√(2)` or
`-√(2)`, so there are both positive and negative values for
`x`.