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?
Select an Answer
and
and
and
and
and
View Correct Answer
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.