find the x and y coordinates

Question

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

Answer 1

The equation of the circle:

x² + y² = 9 EQN1

To find the intersection(s), solve 2 equations in 2 unknowns.

We have y = -2x EQN2, so sub that into EQN1:

x² + (-2x)² = 9

x² + 4x² = 9

x² = 9/5

x = ±3/√5

and

y = -2(±3/√5) = ±6/√5 ( which really should be written "minus-plus"

the points are: (-3/√5, +6/√5) and (+3/√5, -6/√5) Graph the equations to see it.