Question

Type the correct answer in each box.

A circle is centered at the point (-7, -1)
The radius of the circle is

Answer 1

Part 1) The radius is
`r=17\ units`

Part 2) The points (-15,14) and (-15,-16) lies on the circle

Explanation:

The correct question is

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

step 1

Find the radius of the circle

we know that

The distance from the center to any point on the circumference is equal to the radius.

we have

`(-7,-1),(8,7)`

Find the distance

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

substitute

`r=\sqrt{(7+1)^(2)+(8+7)^(2)}\\r=\sqrt{(8)^(2)+(15)^(2)}\\r=√(289)\\r=17\ units`

step 2

The point (-15,y) lies on the circle

we know that

If a ordered pair lie on the circle, them the ordered pair must satisfy the equation of the circle

The equation of the circle is

`(x-h)^(2)+(y-k)^(2)=r^(2)`

The center is (-7,-1) an the radius is 17 units

substitute

`(x+7)^(2)+(y+1)^(2)=17^(2)\\(x+7)^(2)+(y+1)^(2)=289`

substitute the x-coordinate of the point and solve for the y-coordinate

For x=-15

`(-15+7)^(2)+(y+1)^(2)=289\\(-8)^(2)+(y+1)^(2)=289\\64+(y+1)^(2)=289\\(y+1)^(2)=289-64\\(y+1)^(2)=225`

square root both sides

`(y+1)=\pm15\\y=-1\pm15\\y=-1(+)15=14\\y=-1(-)15=-16`

therefore

The points (-15,14) and (-15,-16) lies on the circle

see the attached figure to better understand the problem