determine the point

Question

1.in quad 2 where the line represented by y=-3x intersect the unit circle

Answer 1

y = -3x

 

On unit circle, x^2 + y^2 = 1

 

x^2 = 1 - y^2

 

Substitute this into y = -3x and get

 

y = -3*sqrt(1 - y^2) 

 

y^2 = 9(1 - y^2)

 

10y^2 = 9

 

y = ± 3/sqrt(10)

 

In quadrant 2 use the positive square root.

 

y = 3/√10

 

x = y/(-3) =  (3/√10) / (-3) = -1/√10