Question

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

17, 14

Explanation:

Answer 2

The equation of the circle is

`(x+7)^(2)+(y+1)^(2)=r^(2)`
for some radius
`r`.

We find
`r` by plugging in the point
`(8, 7)`:

`(8+7)^(2)+(7+1)^(2)=r^(2)`

`\rightarrow 15^(2)+8^(2)=r^(2)`

`\rightarrow 225+64=r^(2)`

`\rightarrow 289=r^(2)`

`\rightarrow r=17`

So the radius is 17, and the equation is

`(x+7)^(2)+(y+1)^(2)=289`

For the second part of the question, we plug in
`x=-15`:

`(-15+7)^(2)+(y+1)^(2)=289`

`\rightarrow (-8)^(2)+(y+1)^(2)=289`

`\rightarrow 64+(y+1)^(2)=289`

`\rightarrow (y+1)^(2)=225`

`\rightarrow y+1=\pm 15`

`\rightarrow y=14, -16`

So the answer could either be 14 or -16.