Provide an exact solution and write your solution as a coordinate.

Question

At what point in the third quadrant does the line with equation 𝑦 = 3𝑥 intersect the circle with radius 4 and center at the origin? Provide an exact solution and write your solution as a coordinate.

Answer 1

the circle's equation is x^2 + y^2 = 16

plug in y= 3x to get

x^2 + 9x^2 = 16

10x^2 = 16

x^2 = 16/10

x = -4/sqr10

y=-12/sqr10

the intersection point is (-4sqr10, -12sqr10)