Question

A circle has center O(5, −1) and radius 5. Which of the following points is on the circle?

Answer 1

Answer:

The correct answer is the first one listed.

Step-by-step explanation:

First you have to determine what the equation for that circle is.  The standard form of a circle is

$(x-h)^2+(y-k)^2=r^2$ where h and k are the coordinates of the center and the radius is squared.  Using the given info, our equation will look like this:

$(x-5)^2+(y+1)^2=25$

Now we use the coordinates given and plug in 2 for x and 3 for y and do the math and see if the 2 sides are equal.

$(2-5)^2+(3+1)^2=25$

and 9 + 16 = 25, right?  So that's how you can check the other coordinate pairs to verify that they DON'T work out!