Write the equation of a circle given that the endpoints of the diameter are (5, –4) and (–7, 4).

Question

Hi! Please help me understand this, and also please provide a solution.

Thanks!

Answer 1

Hi Blythe,

Think about a circle. The every diameter that can be drawn runs through the center point. And the center point of the diameter is the midpoint of the diameter, so the center of the circle is at the midpoint of the diameter. So find the midpoint between those two endpoints.

( [5+(-7)]/2, [(-4)+4]/2) = (-2/2, 0/2) so the midpoint is at (-1,0) and that means the center of the circle is at (-1,0).

To write the equation of the circle, one needs the coordinates of the center point (see above) and the radius.

The radius length is the distance from the center point to a point on the circle. And we have been given two different points on the circle, so choose one of them and find the distance between the center and the point you chose.

Using (5, -4) and (-1,0) the distance is sqrt{ [5-(-1)]²+[(-4)-0]² } = sqrt(36 + 16) = sqrt(52)

Equation of a circle is (x-h)² + (y-k)² = r²

Using our numbers this would be: [x-(-1)]² + [y-0]² = [√52]²

or (x+1)² + y² = 52