The equation of the circle centered at (3,5) and passing through point (-2,9) is given by:
(x - 3)² + (y - 5)² = 41.
What is the equation of a circle?
The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
For the circle graphed, we have that the circle is at (3,5), hence [tex]x_0 = 3, y_0 = 5[/tex].
Then:
(x - 3)² + (y - 5)² = r²
The line passes through point (-2,9), that is, when x = -2, y = 9, hence the radius is found as follows:
(x - 3)² + (y - 5)² = r²
r² = (-2 - 3)² + (9 - 4)²
r² = 41.
Hence the equation is:
(x - 3)² + (y - 5)² = 41.
More can be learned about the equation of a circle at https://brainly.com/question/24307696
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