Question

Type the correct answer in each box.

A circle is centered at the point (-7, -1) and passes through the point (8, 7).

The radius of the circle is_____ units. The point (-15, ___) lies on this circle.

Answer 1

1. r=17

2. (-15,14) or (-15,-16)

Explanation:

The radius of the circle is the distance from the center to the point on the circle, thus

`r=√((8-(-7))^2+(7-(-1))^2)=√(15^2+8^2)=√(225+64)=√(289)=17.`

The equation of the circle is

`(x-(-7))^2+(y-(-1))^2=r^2\\ \\(x+7)^2+(y+1)^2=289.`

If point lies on this circle, then its coordinates satisfy the circle's equation:

`(-15+7)^2+(y+1)^2=289\\ \\64+(y+1)^2=289\\ \\(y+1)^2=225\\ \\y+1=15\text{ or }y+1=-15\\ \\y=14\text{ or }y=-16`