Answer:
(x +10)² +(y +4)² = 200
Explanation:
You want the equation of the circle with center (-10, -4) that goes through point (4, -2).
Circle
The standard equation of a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
Application
The equation of the circle with center (-10, -4) will be of the form ...
(x -(-10))² +(y -(-4))² = r²
(x +10)² +(y +4)² = r²
We know that point (4, -2) satisfies this equation, so we can substitute those values for (x, y) and find the value of r²:
(4 +10)² +(-2+4)² = r²
14² +2² = r² = 196 +4 = 200
Using this value in the circle equation, we have ...
(x +10)² +(y +4)² = 200
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Additional comment
The equation written by a graphing program for the circle with the given center and point is in agreement with the above.