Answer:
Explanation:
The equation of a circle in the Cartesian coordinate system with center \((h, k)\) and radius \(r\) is given by the formula:
\[(x - h)^2 + (y - k)^2 = r^2\]
In your case, the center of the circle is \((-2, -3)\), and it contains the point \((4, 5)\). To find the radius (\(r\)), you can use the distance formula between two points:
\[r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]
Let's substitute the given values:
\[r = \sqrt{(4 - (-2))^2 + (5 - (-3))^2}\]
\[r = \sqrt{6^2 + 8^2}\]
\[r = \sqrt{36 + 64}\]
\[r = \sqrt{100}\]
\[r = 10\]
Now, substitute the center and radius into the circle equation:
\[(x - (-2))^2 + (y - (-3))^2 = 10^2\]
\[(x + 2)^2 + (y + 3)^2 = 100\]
So, the equation of the circle is \((x + 2)^2 + (y + 3)^2 = 100\).