In the xy-plane, a line parallel to the x-axis intersects the y-axis at the point (0, 4). This line also intersects a circle in two points. The circle has a radius of 5 and its center is at the origin. What are the coordinates of the two points of intersection?
A)(1, 2) and (2, 1)
B)(2, 1) and (2, -1)
C)(3, 4) and (3, -4)
D)(3, 4) and (-3, 4)
E)(5, 0) and (-5, 0)

Question

Quizplus · Accepted Answer

A line parallel to the x-axis and intersecting the y-axis at (0, 4) is a horizontal line with y=4. The circle's equation is x^2 + y^2 = 25 (since its radius is 5 and it's centered at the origin). Substituting y=4 into the circle's equation gives x^2 + 16 = 25, which simplifies to x^2 = 9. Solving for x gives x = 3 and x = -3, so the points of intersection are (3, 4) and (-3, 4).

In the Xy-Plane, a Line Parallel to the X-Axis Intersects