ACT question equations of circles and finding x-intercepts

Question

A circle with the equation x² + y² = 16 is graphed in the standard (x,y) coordinate plane. At what points

does the circle intersect the x-axis?

F. (−2,0) and (2,0)

G. (−4,0) and (4,0)

H. (−8,0) and (8,0)

J. (−16,0) and (16,0)

K. (−32,0) and (32,0)

Answer 1

The graph intersects the x-axis when y = 0.

So, x² + (0)² = 16.

x = 4 or -4

The graph intersects the x-axis at (4,0) and (-4,0).

Answer 2

The general equation of a circle is (x - h)² + (y - k)² = r² where (h, k) is the center and r is the radius. For the given equation, the Center is (0,0) and the Radius is 4.

To graph this, plot the center first and then go 4 units up, down, right, and left. Here is the graph.

The circle intersects the x-axis at (-4, 0) and (4, 0). So the answer is G.

Answer 3

This question is asking for an understanding of 2 concepts, the equation of a circle and x-intercepts.

*First the equation of a circle (x-h)² + (y-k)² = r² where (h,k) is the center and r is the radius

In this particular circle, the center is (0,0) the origin, and the radius is 4.

**To answer the question "At what points does the circle intersect the x-axis?" we need to know that the points on the x-axis have a y coordinate of 0. So replace y = 0 in the equation and simplify

x² + (0)² = 16

x² = 16

x² = 4²

x = 4 or x = -4 The points where the circle intersects the x-axis are (-4, 0) and (4, 0)