How do you find the equation of a circle?

Answer 1

A circle is the locus of all points equidistant from a fixed point on the plane. The fixed point is called the centre of the circle and the equal distance is called the radius of the circle.

We can derive the equation of the circle from the distance formula.

Let O be the centre of the circle and r be the radius of the circle.

Here the centre = Origin = (0, 0) and the radius = r units.

The distance r = sqrt ((x-0)2 + (y-0)2)

r = sqrt (x2 + y2)

Squaring both the sides, we get x2 + y2 = r2

This is the equation of the circle with centre as Origin.

If the centre point is some (h, k), then use the distance formula to find the radius r.

The distance r = sqrt ((x-h)2 + (y-k)2)

Squaring both sides, we get (x-h)2 + (y-k)2 = r2.

This is the equation of the circle with centre as the point (h, k).