The point (-1,0) lies on a circle whose center is at (-6,5). Find an equation of this circle
You know the equation must be
(x+6)^2 + (y-5)^2 = r^2
sub in the other point (-1,0)
25 + 25 = r^2 = 50
so (x+6)^2 + (y-5)^2 = 50
Thanks!! for the help
To find the equation of a circle, you need two key pieces of information: the coordinates of the center and the radius of the circle.
Given that the center of the circle is (-6, 5), we have the center coordinates (h, k) = (-6, 5).
The distance formula can be used to find the radius of the circle. The formula is:
r = sqrt((x2 - x1)^2 + (y2 - y1)^2)
We can use the point (-1, 0) as (x2, y2), and (-6, 5) as (x1, y1) in the formula:
r = sqrt((-1 - (-6))^2 + (0 - 5)^2)
= sqrt((5)^2 + (-5)^2)
= sqrt(25 + 25)
= sqrt(50)
= 5sqrt(2)
Now that we have the center coordinates and the radius, we can write the equation of the circle in the standard form:
(x - h)^2 + (y - k)^2 = r^2
Plugging in the values, we get:
(x - (-6))^2 + (y - 5)^2 = (5sqrt(2))^2
(x + 6)^2 + (y - 5)^2 = 50
Therefore, the equation of the circle is (x + 6)^2 + (y - 5)^2 = 50.