Here’s How to Crack It
Start by building what you know of the circle formula: If the center is at point (2, 0), then the circle
equation will be (x − 2)^2 + (y – 0)^2 = r^2 , or more simply, (x − 2)^2 + y^2 = r^2 . Choices (B) and (D) do not
match, so eliminate them.
Now calculate the radius of the circle. Find the distance between points (2, 0) and (5, ) by drawing a
right triangle. The base of the right triangle will be the difference between the x values of 5 and 2, so the
base of the right triangle is 3. The height of the right triangle will be the difference between the y values,
which is . Use the Pythagorean Theorem to find the hypotenuse of the triangle, which will be the
distance between the points (and, therefore, the length of the radius). So, r^2 = 3^2 + ( )^2 = 9 + 7 = 16.
Since you have the value of r^2 , which is 16, use POE to eliminate (A) and select (C).
Just as you may be given a parabola in standard form and expected to convert it into vertex form, you may
also be given an equation for a circle that is not in the form (x – h)^2 + (y – k)^2 = r^2 and expect you to
figure out the radius or center. To do so, you just need to complete the square as you did above with the
equation of a parabola. You will need to do it twice, though—once for the x-terms and again for the y-
terms.