Find the equation of a circle with centre (-3, -8) and radius \(4\sqrt{6}\).
Question 1 Report
Find the equation of a circle with centre (-3, -8) and radius \(4\sqrt{6}\).
Answer Details
To find the equation of a circle with center \((a, b)\) and radius \(r\), we use the formula:
\[(x - a)^2 + (y - b)^2 = r^2\]
In this case, the center is \((-3, -8)\) and the radius is \(4\sqrt{6}\). So the equation of the circle is:
\[(x - (-3))^2 + (y - (-8))^2 = (4\sqrt{6})^2\]
which simplifies to:
\[(x + 3)^2 + (y + 8)^2 = 96\]
Expanding the left-hand side gives:
\[x^2 + 6x + 9 + y^2 + 16y + 64 = 96\]
which simplifies to:
\[x^2 + y^2 + 6x + 16y - 23 = 0\]
So the answer is (2) \(x^{2} + y^{2} + 6x + 16y - 23 = 0\).
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