How to find the Equation of a Circle if the coordinates of its center and the length of its radius are given.
EXAMPLE 2: What is the equation of a circle whose center is (8,3) and radius is 2 units?
SOLUTION:
The standard equation of a circle is:
(x – h)² + (y – k)² = r² ——–(1)
where (h, k) is the coordinate of center of the circle and r is the radius.
Here center (h, k) = (8, 3)
which implies
h = 8 and
k = 3
radius = r = 2 units
Put values of h, k and r in equation (1)
(x – h)² + (y – k)² = r²
(x – 8)² + (y – 3)² = 2²
(x – 8)² + (y – 3)² = 4
This is the standard equation of the circle whose center is at (8, 3) and radius is 2 units.
This standard equation can be written as general equation (or simply an equation) of a circle whose center is at (8, 3) and radius is 2 units by squaring the terms, then simplifying.
(x – 8)² + (y – 3)² = 4
x² + 64 – 16x + y² + 9 – 6y = 4
x² + y² – 16x – 6y + 64 + 9 – 4 = 0
x² + y² – 16x – 6y + 69 = 0
This is the general equation (or simply an equation) of a circle whose center is (8,3) and radius is 2 units.
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