Question

Type the correct answer in each box.

Answer 1

Answer:

1. r=17

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

Step-by-step explanation:

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

$r=\sqrt{(8-(-7))^2+(7-(-1))^2}=\sqrt{15^2+8^2}=\sqrt{225+64}=\sqrt{289}=17.$

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:

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