Question

13 A circle has center (2,5) and goes through (9,29).

Answer 1

The equation of the circle is (x - 2)^2 + (y - 5)^2 = 625.

Step-by-step explanation:

A circle has the special property that the distance from its center to any point on the circle is the same. To find the equation of a circle, we can use the formula (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. In this case, the center is (2,5) and it goes through the point (9,29). We can substitute these values into the equation and solve for the radius:

(9 - 2)^2 + (29 - 5)^2 = r^2

7^2 + 24^2 = r^2

49 + 576 = r^2

625 = r^2

Therefore, the equation of the circle is: (x - 2)^2 + (y - 5)^2 = 625.