11. Find the equation for the circle with center (−2,4) and passing through (5,−3).

Answer:
In standard form: (x+2)² + (y-4)² = 98
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 d = \sqrt{(-2 - 5)^2 + (4-(-3))^2}[/tex]
[tex]\rightarrow \sf d = \sqrt{(-7)^2 + (7)^2}[/tex]
[tex]\rightarrow \sf d = 7\sqrt{2}[/tex]
Equation of circle: