How do I find the area of a circle using points with variables?

Question

This is the whole question.

On a coordinate plane, a circle passes through the points (x, y) and (-x, y). Which of the following represents the area of the circle?

 

A. 4πx

B. πx²/4

C. πx²

D. 4x²

Answer 1

Michael, aren't you assuming that the two points are endpoints of a diameter? They could just as well be endpoints of some chord, and thus you cannot know the radius.

 

From the wording of the question, it's implied that this is a multiple choice question; perhaps the student has left out those choices, or possibly more info was also lost.

Answer 2

Assuming the diameter of the circle is a horizontal line (being that y is same for both points), the diameter of the circle will be 2x.  Therefore, the radius is x.

 

The area of any circle is     A = πr²

 

In this circle, the area is        A = πx²