The line with equation is graphed on the same as the circle with center and radius . What are the of the points of intersection of the line and the circle?

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For this question, it may help to draw a diagram.

The line intersects the circle in points. These two points and the center of the circle form a triangle with two sides of length (since the radius of the circle is ) and with height . (The distance between the point and the line is the distance between and .)

Using the Pythagorean Theorem, you can find that . Point has . Therefore, the of the points of intersection are and or and . The correct answer is D.

You could also solve the problem algebraically. A circle with center and radius has equation . Substitute into the equation, and it simplifies to . Solving for produces the two of the points of intersection of the circle and the line.