Question

5
сл
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

Part 1: Finding radius

The radius of a circle is defined as the distance from the center to a point on the circle's circumference.

Using the distance formula,

$r=\sqrt{(-7-8)^{2}+(-1-7)^{2}}=\boxed{17}$

Part 2: Finding the point with x-coordinate -15

Let the y coordinate of the point be y. Then, we have the point (-15, y). Substituting into the distance formula,

$\sqrt{(-15-(-7))^{2}+(-1-y)^{2}}=17\\\\64+(-1-y)^{2}=289\\\\(-1-y)^{2}=225\\\\-1-y =\om 15\\\\y=\boxed{-16, 14}$