# What is the equation of a circle that has a radius of 6 and passes through the points (3, 9) and (3, -3)

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justaguide | Certified Educator

The equation of a circle that has a radius 6 and which passes through the points (3, 9) and (3, -3) has to be determined.

The radius of the circle is 6, this gives its diameter as 12. The distance between the points (3, 9) and (3, -3) is also equal to 12. This gives the center of the circle as a point lying halfway between the points (3, 9) and (3, -3). The center of the circle is `((3 +3)/2, (9 - 3)/2)` or (3, 3)

The equation of a circle with radius r and center (h, k) is `(x - h)^2 + (y - k)^2 = r^2` . Substituting the values derived, the equation of the required circle is:

`(x - 3)^2 + (y - 3)^2 = 36`

**The equation of the circle with radius 6 and which passes through the points (3, 9) and (3, -3) is **`(x - 3)^2 + (y - 3)^2 = 36`