Question

PLS HELP!!

A circle is centered at 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) The radius of the circle is

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

Explanation:

Answer 2

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

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

Explanation:

Part 1

we know that

The distance between the center of the circle at point (-7,-1) and the point (8,7) is equal to the radius of the circle

so

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

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

substitute the values

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

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

`r=√(289)}`

`r=17\ units`

Part 2

we know that

If the point (-15,y) lies on the circle, then the ordered pair must be satisfy the equation of the circle

The equation of the circle is equal to

`(x+7)^(2)+(y+1)^(2)=17^(2)` -----> equation of the circle in center radius form

substitute the value of x=-15 in the equation and solve for y

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

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

`(y+1)^(2)=289-64`

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

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

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

so

`y=14`

`y=-16`

therefore

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

see the attached figure to better understand the problem