Question

Which of the following is the equation of a circle whose center is at the origin and whose diameter has end (-1,2) and (1,-2)

Answer 1

Answer:

x² + y² = 5

Step-by-step explanation:

The circle with center (h, k) and radius r has equation ...

... (x -h)² + (y -k)² = r²

You can find r² using the Pythagorean theorem or the distance formula, or you can simply calculate what it needs to be to make one or the other of the points lie on the circle.

For (h, k) = (0, 0), the equation is ...

... (x -0)² + (y -0)² = r²

Using (-1, 2) for (x, y), we can find r² as ...

... (-1 -0)² + (2 -0)² = r² = 1 + 4 = 5

Then the circle equation is ...

... x² + y² = 5