Answer:
(x - 11)² + (y + 8)² = 74
Step-by-step explanation:
The equation takes the form (x - h)² + (y - k)² = r², where h is the x coordinate, k is the y coordinate of the center and r is the radius of the circle.
The center of circle is the middle of diameter.
The radius is the distance between the center and any point from the circumference of a circle.
The middle of diameter:
[tex]\left(\frac{18+4}2\,;\,\frac{-13-3}2\right)=\left(\frac{22}2\,;\,\frac{-16}2\right)= \left(11\,;-8\right)[/tex] ⇒ h = 11, k = -8
The distance between the center and point (4,-3)
[tex]r=\sqrt{(11-4)^2+(-8-(-3))^2}=\sqrt{7^2+(-5)^2}=\sqrt{49+25}=\sqrt{74}[/tex]
so the equation:
(x - 11)² + (y - (-8))² = (√74)²
(x - 11)² + (y + 8)² = 74
