11. Find the equation for the circle with center (−2,−3) and passing through (1,5).
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Answer:
(x +2)² + (y+3)² = 73
Use the distance formula to find radius:
[tex]\sf d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
where (x1, y1), (x2, y1) are points
[tex]\rightarrow \sf \sqrt{(-2-1)^2+(-3-5)^2}[/tex]
[tex]\rightarrow \sf \sqrt{73}[/tex]
Eqaution of circle:
(x-h)² + (y-k)² = r²
(x-(-2))² + (y-(-3))² = (√73)²
(x +2)² + (y+3)² = 73