Question

1. Find the equation of the circle that has a line segment with end points (18,-13) and (4,-3) as the circle diameter. The equation takes the form (x - h)2 + (y - k)2 = 2. Where h is the x coordinate, k is the y coordinate of the center and r is the radius of the circle. h = k =​

Answer 1

(x - 11)² + (y + 8)² = 74

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:

`\left(\frac{18+4}2\,;\,\frac{-13-3}2\right)=\left(\frac{22}2\,;\,\frac{-16}2\right)= \left(11\,;-8\right)` ⇒ h = 11, k = -8

The distance between the center and point (4,-3)

`r=√((11-4)^2+(-8-(-3))^2)=√(7^2+(-5)^2)=√(49+25)=√(74)`

so the equation:

(x - 11)² + (y - (-8))² = (√74)²

(x - 11)² + (y + 8)² = 74