The equation of the circle is:
[tex](x + 4)^2 + (y + 2)^2 = 17^2[/tex]
The general equation for a circle of radius R and center (a, b) is:
[tex](x - a)^2 + (y - b)^2 = R^2[/tex]
Here the center is (-4, -2), and it contains the point (4, -17), so the radius is:
[tex]R = \sqrt{(4 - (-4))^2 + (-2 + 17)^2} = 17[/tex]
So the equation of the circle is:
[tex](x + 4)^2 + (y + 2)^2 = 17^2[/tex]
If you want to learn more about circles:
https://brainly.com/question/1559324
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