To solve this question, we have to find the equation of the circle with given center and where it passes. Doing this, we get that the equation of the circle is:
[tex](x - 16)^2 + (y - 30)^2 = 1156[/tex]
Equation of a circle:
The equation of a circle with 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]
Center at (16, 30)
This means that [tex]x_0 = 16, y_0 = 30[/tex]
Thus
[tex](x - 16)^2 + (y - 30)^2 = r^2[/tex]
Passes through the origin:
We use this to find the radius squared, as this means that [tex]x = 0, y = 0[/tex] is part of the circle. Thus
[tex](x - 16)^2 + (y - 30)^2 = r^2[/tex]
[tex](0 - 16)^2 + (0 - 30)^2 = r^2[/tex]
[tex]r^2 = 16^2 + 30^2 = 1156[/tex]
Thus, the equation of the circle is:
[tex](x - 16)^2 + (y - 30)^2 = 1156[/tex]
For another example to find the equation of a circle, you can look at https://brainly.com/question/23719612
