The equation represents a circle centered at (3,5) and passing through the point (-2,9) will be,[tex]\rm x^2+y^2 -6x-10y-7=0[/tex]
What exactly is a circle?
It is a point locus drawn equidistant from the center. The radius of the circle is the distance from the center to the circumference.
Given data;
The Centre of the circle is,(h,k)=(3,5)
The circle traverses (-2,9). Consequently, the radius of the circle r is equal to the separation between (3, 4) and (-2,1).
So radius;
[tex]r = \sqrt{{{(x_2-x_1)^2 + (y_2-y_1)^2}}[/tex]
[tex]r = \sqrt{{(9-5)^2+(3+2)^2 }[/tex]
[tex]r=\sqrt {41} \\\\ r =6.1 \ units[/tex]
Now equation of the circle with center (h,k) and radius r is
[tex]\rm (x-h)^2 + (y-k)^2 = r^2\\\\ (x-3)^2 + (y-5)^2 = (\sqrt{41})^2\\\\ x^2 - 6x + 9 + y^2 - 10y + 25 = 41[/tex]
[tex]x^2+y^2 -6x-10y-7=0[/tex]
Hence equation represents a circle that will be,[tex]x^2+y^2 -6x-10y-7=0[/tex]
To learn more about the circle, refer to the link: https://brainly.com/question/11833983.
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