Question

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=2.5x+2 intersect the circle with radius 6 and center (0, 2)?

Answer 1

x² + ((1.5x + 3) - 3)² = 16
x² + (1.5x)² = 16
x² + 2.25x² = 16
3.25x² = 16
x = 8√(13)/13
x ≈ 2.219
and so
y = 1.5(8√(13)/13)+ 3
≈ 6.328
so
(2.219, 6.328)