Answer:
(x - 9)^2 + (y + 5)^2 = 50.
Explanation:
To determine the equation of the circle with a center at (9, -5) and containing the point (10, 2), we need to find the radius of the circle first. The radius is the distance between the center and any point on the circle, such as (10, 2).
We can use the distance formula to find the radius:
r = √((x2 - x1)^2 + (y2 - y1)^2)
Substituting the given values:
r = √((10 - 9)^2 + (2 - (-5))^2)
Simplifying:
r = √(1^2 + 7^2)
r = √(1 + 49)
r = √50
Simplifying further:
r = √(25 * 2)
r = 5√2
Now that we have the radius, we can write the equation of the circle in standard form:
(x - h)^2 + (y - k)^2 = r^2
Substituting the values:
(x - 9)^2 + (y - (-5))^2 = (5√2)^2
Simplifying:
(x - 9)^2 + (y + 5)^2 = 50
Therefore, the equation of the circle with a center at (9, -5) and containing the point (10, 2) is:
(x - 9)^2 + (y + 5)^2 = 50.