This problem came up today in a tutoring session. Circle questions are showing up once or twice on each new SAT test. My student was flummoxed on how to solve it. She had forgotten the formula for the equation of a circle so she had no idea how to answer this question. Unfortunately, the SAT doesn’t list this formula in the handy little section at the front where they list other formulas.
It’s worth memorizing the formula for a circle (if you want to scores in the 600s.)
I don’t like forcing my students to memorize information without any context. There’s a great explanation of this why this is the equation of a circle over at Math is Fun. Sal Khan over at Khan Academy has a video explanation of the equation of a circle.
And you also need to know the distance formula in order to calculate the radius. (And they don’t give you the distance formula either on in the reference section.)
Here’s how to solve this question.