Write the equation of each circle.
Center at (-1,8) passes through (9,3)
easiest way:
centre is (-1,8) , so the equation is
(x+1)^2 + (y-8)^2 = r^2
sub in the given point (9,3)
r^2 = 10^2 + (-5)^2 = 125
(x+1)^2 + (y-8)^2 = 125
Write an equation for a circle with center at (–8, 4) and diameter 2.
To write the equation of the circle, we can use the equation of a circle, which is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) represents the center of the circle, and r represents the radius.
Given that the center is (-1, 8) and it passes through (9, 3), we can determine the radius using the distance formula between two points:
r = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the radius first:
r = sqrt((9 - (-1))^2 + (3 - 8)^2)
= sqrt(10^2 + (-5)^2)
= sqrt(100 + 25)
= sqrt(125)
= 5√5
Now we have the center (-1, 8) and the radius 5√5, we can plug these values into the equation of a circle:
(x - (-1))^2 + (y - 8)^2 = (5√5)^2
(x + 1)^2 + (y - 8)^2 = 25 * 5
(x + 1)^2 + (y - 8)^2 = 125
Therefore, the equation of the circle is (x + 1)^2 + (y - 8)^2 = 125.