Equation of a circle. Find the equation of a circle with center (5,-2) and radius 16. Solution The equation of a circle with center (a, b) and radius r is (x - a)^2 + (y - b)^2 = r^2 Here the center is (5, -2) and the radius is 16 => (x - 5)^2 + (y + 2)^2 = 16^2 => x^2 + 25 - 10x + y^2 + 4 + 4y = 256 => x^2 + y^2 - 10x + 4y - 227 = 0 The equation of the required circle is x^2 + y^2 - 10x + 4y - 227 = 0.

1. Equation of a circle.
Find the equation of a circle with center (5,-2) and radius 16.
Solution
The equation of a circle with center (a, b) and radius r is (x - a)^2 + (y - b)^2 = r^2
Here the center is (5, -2) and the radius is 16
=> (x - 5)^2 + (y + 2)^2 = 16^2
=> x^2 + 25 - 10x + y^2 + 4 + 4y = 256
=> x^2 + y^2 - 10x + 4y - 227 = 0
The equation of the required circle is x^2 + y^2 - 10x + 4y - 227 = 0