Write an equation of a circle with diameter AB.A(0,0),B(-6,8)
To write the equation of a circle with diameter AB, we need to find the center and radius of the circle first.
The center of the circle is the midpoint of the line segment AB, which can be found by averaging the x-coordinates and y-coordinates of points A and B.
Center coordinates:
x-coordinate = (x-coordinate of A + x-coordinate of B) / 2
= (0 + (-6)) / 2 = -3
y-coordinate = (y-coordinate of A + y-coordinate of B) / 2
= (0 + 8) / 2 = 4
So, the center of the circle is C(-3, 4).
The radius of the circle is half the length of AB, which can be found using the distance formula:
Distance = √((x2 - x1)² + (y2 - y1)²)
Distance = √((-6 - 0)² + (8 - 0)²)
= √((-6)² + 8²)
= √(36 + 64)
= √100
= 10
Thus, the radius of the circle is 10.
Now we can write the equation of the circle using the center and radius information:
(x - h)² + (y - k)² = r²
where (h, k) is the center of the circle and r is the radius.
Substituting the values we found:
(x - (-3))² + (y - 4)² = 10²
(x + 3)² + (y - 4)² = 100
Therefore, the equation of the circle with diameter AB is (x + 3)² + (y - 4)² = 100.