Question

Recall the equation for a circle with center ( h , k ) (h,k) and radius r r. At what point in the first quadrant does the line with equation y = 2.5 x + 2 y=2.5x+2 intersect the circle with radius 6 and center (0, 2)?

Answer 1

equation of this circle is
x^2 + (y - 2)^2 = 36
y = 2.5x + 2

Substitute for y in the equation of the circle:-

x^2 + (2.5x + 2 - 2)^2 = 36

x^2 + 6.25x^2 = 36

x^2 = 36 / 7.25

x = +/- 6 / 2.693 = +/- 2.228

when x = 2.228 y = 2.5(2.228) + 2 = 7.57 to nearest hundredth

when x = -2.228 y = 2.5(-2.228) + 2 = -3.57

So they intersect at 2 points but the intersect in the first quadrant is at (2.23, 7,57) to nearest hundredth.