Answer: Choice B. (-3, 3)
Work Shown
[tex]x^2 + y^2 = 18\\\\x^2 + (x+6)^2 = 18\\\\x^2 + x^2+12x+36 = 18\\\\x^2 + x^2+12x+36-18 = 0\\\\2x^2+12x+18 = 0\\\\[/tex]
[tex]2(x^2+6x+9) = 0\\\\2(x+3)^2 = 0\\\\(x+3)^2 = 0\\\\x+3 = \sqrt{0}\\\\x+3 = 0\\\\x = -3\\\\[/tex]
If x = -3, then,
[tex]y = x+6\\\\y = -3+6\\\\y = 3[/tex]
This indicates that (-3,3) is the intersection point of the circle [tex]x^2+y^2 = 18[/tex] and the line y = x+6. It turns out that this is a tangent line since it intersects the circle at exactly one point. See the diagram below.
