Question

Recall the equation for a ˚le with center (h, k) and radius r. At what point in the first quadrant does the line with the equation y = 0.5x + 3 intersect the ˚le with a radius of 6 and center (0, 3)?

A) (2, 4)
B) (3, 6)
C) (4, 8)
D) (5, 10)

Answer 1

To find the point of intersection between the line y = 0.5x + 3 and the circle with radius 6 and center (0, 3), substitute the equation of the line into the equation of the circle and solve for x and y.

Step-by-step explanation:

To find the point of intersection between the line y = 0.5x + 3 and the circle with radius 6 and center (0, 3), we substitute the equation of the line into the equation of the circle:

0.5x + 3 = sqrt((x-0)^2 + (y-3)^2)

Simplifying the equation by squaring both sides, we get:

0.25x^2 + 3x + 9 = x^2 + 6x + 9

0.75x^2 - 3x = 0

Dividing both sides by x, we get:

0.75x - 3 = 0

Solving for x, we find x = 4. Substituting x = 4 into the equation of the line, we find y = 0.5(4) + 3 = 5. Therefore, the point of intersection is (4, 5).