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

Well, the answer would be 17,23 Also i had the same question as you so i already know the answer

Answer 2

17, 23

Explanation:

First, to find the radius, we need to find the distance between the center of the circle, (-7, -1), and the point that the circle passes through, (8, 7). Plugging these coordinates into the distance formula we do
`√((-7-8)^2+(-1-7)^2)` which gives us 17. Therefore, the radius of the circle is 17 units.

Next to find the y-coordinate of the point (-15, ), we need to write out the equation of the circle and then plug in the point. The equation of the circle would be
`(x+7)^(2) +(y-8)^(2)=289`. Now we can plug in -15 for x and solve for y. So now we have
`(-15+7)^(2) +(y-8)^(2)=289`.

Simplifying the equation we have
`(8)^(2) +(y-8)^(2)=289`. Subract
`8^(2)` from 289 and now the equation is
`(y-8)^(2)=225`. Square root both sides to get
`y-8=15`. We solve for y to get 23. Therefore, the point is (-15, 23).