Recall the equation for a circle with center ( h , k ) and radius r . At what point in the first quadrant does the line with equation y = x + 3 intersect the circle with radius 6 and center (0, 3)?

Question

x=

y=

Thanks!

Answer 1

they intersect at (3sqr2, 3+3sqr2) in the 1st quadrant

x = 3sqr2 = about 4.24

y = 3+3sqr2 = about 7.24

x^2 + (y-3)^2 = 36

y = x+3

x^2 + (x+3-3)^2 = 36

2x^2 = 36

x^2 = 36/2

x = 6/sqr2 = 3sqr2

y = 3+3sqr2

there's also a 2nd intersection in the 3rd quadrant

(-3sqr2, -3-3sqr2)