Equation of the circle:
[tex](x-5)^2+(y+4)^2=100[/tex]
Step-by-step explanation:
The equation of a circle is given by
[tex](x-x_0)^2+(y-y_0)^2=r^2[/tex]
where
[tex](x_0,y_0)[/tex] are the coordinates of the center of the circle
r is the radius of the circle
For the circle in this problem, we know that:
(5,4) are the coordinates of the center
We also know that the circle passes through the point (-3,2), therefore we can calculate the radius as the distance between the point on the circle and the center of the circle:
[tex]r=\sqrt{(-3-(5))^2+(2-(-4))^2}=\sqrt{(-8)^2+(6)^2}=\sqrt{64+36}=10[/tex]
Therefore, the equation of the circle is:
[tex](x-5)^2+(y-(-4))^2=10^2\\(x-5)^2+(y+4)^2=100[/tex]
Learn more about circles:
brainly.com/question/4713715
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