Recall the equation for a circle with center ( h , k ) and radius r

Question

Recall the equation for a circle with center  and radius . At what point in the first quadrant does the line with equation  intersect the circle with radius 3 and center (0, 2)?

 = 

 = 

Answer 1

x= 3/sqr5

y = 6/sqr5 +2

x^2 + (y-2)^2 = 9

y-2 = sqr(9-x^2)

y = 2+sqr(9-x^2) = 2x+2

2x = sqr(9-x^2)

4x^2 = 9-x^2

5x^2 = 9

x^2 = 9/5

x = 3/sqr5

y = 2(3/sqr5)+2

y = 6/sqr5 +2

there's a 2nd intersection, but not in the 1st quadrant, so ignore the negative square roots.