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

plato users the answer is 17 units and (-15,14)

Explanation:

Answer 2

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

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

Explanation:

step 1

Find the radius of the circle

we know that

To find the radius of the circle calculate the distance between the center of the circle and the point (8,7)

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

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

we have

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

substitute

`r=\sqrt{(7+1)^(2)+(8+7)^(2)}`

`r=\sqrt{(8)^(2)+(15)^(2)}`

`r=√(289)`

`r=17\ units`

step 2

Find the equation of the circle

The equation of the circle in standard form is equal to

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

where

(h,k) is the center

r is the radius

substitute

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

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

step 3

Find the y-coordinate of the point (-15.y)

substitute the x-coordinate in the equation of the circle and solve for y

`(-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)=(+/-)15`

`y=-1(+/-)15`

`y1=-1(+)15=14`

`y2=-1(-)15=-16`

therefore

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

see the attached figure to better understand the problem