Find the points where the line y=−3x intersects a circle of radius 4 centered at the origin. Give exact values for the x and y coordinates.

Answer 1

the circle equation is:

x^2 + y^2 = 16

x^2 + (-3x)^2 = 16

x^2 + 9x^2 = 16

10x^2 =16

x^2 = 16/10

x = sqr1.6 = about 1.265

y=-3x =-3sqr1.6 =-3.795

the two points of intersection are

(sqr1.6, -3sqr1.6) and (-sqr1.6, 3sqr1.6) or

(1.265, -3.795), and (-1.265, 3.795)