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=0.5x+4 intersect the circle with radius 4 and center (0,4)

Answer 1

9514 1404 393

Answer:

≈ (3.578, 5.789)

Explanation:

We can substitute for y and solve for x.

(x -h)^2 +(y -k)^2 = r^2 . . . equation of a circle with center (h, k), radius r

x^2 +(y -4)^2 = 4^2 . . . . . . the equation of the given circle

x^2 +((0.5x +4) -4)^2 = 16

(5/4)x^2 = 16

x = 8/5√5 . . . . multiply by 4/5 and take the square root

y = 0.5x +4

y = 4/5√5 +4

The point of intersection is (8/5√5, 4+4/5√5), approximately (3.578, 5.789).