The equation of the circle with center (−1,−2) containing the point (0,6).
(x + 1)^2 + (y + 2)^2 = 65
How to determine the equation of the circle?
Remember that the equation of a circle with radius R and center (a, b) is written as:
(x - a)^2 + (y - b)^2 = R^2
Here we know that the center of the circle is (-1, -2), then our equation is something like:
(x + 1)^2 + (y + 2)^2 = R^2
We know that our circle contains the point (0, 6), replacing these values in the equation above we get:
(0 + 1)^2 + (6 + 2)^2 = R^2
1 + 8^2 = R^2
65 = R^2
Then the circle equation is:
(x + 1)^2 + (y + 2)^2 = 65
Learn more about circle equations:
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