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

Radius is the distance from the centre to any point in the circumference. i.e. radius =
`\sqrt{ (-7-8)^(2) + (-1-7)^(2) } = \sqrt{ (-15)^(2) + (-8)^(2) } \\ = √(225+64) = √(289) =17`
radius = 17 units

Answer 2

The radius of the circle is 17 units. The point (-15,-16) or (-15,14) lies on this circle.

Explanation:

It is given that the circle is centered at the point (-7, -1) and passes through the point (8, 7).

Distance formula:

`D=√((x_2-x_1)^2+(y_2-y_1)^2)`

Using distance formula we get,

`r=√((8-(-7))^2+(7-(-1))^2)`

`r=√((15)^2+(8)^2)`

`r=17`

The radius of the circle is 17 units.

Let the circle passing through the point (-15,y).

`r=√((-15-(-7))^2+(y-(-1))^2)`

`17=√(64+(y+1)^2)`

Taking square root both the sides.

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

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

`225=(y+1)^2`

Taking square root both the sides.

`\pm √(225)=(y+1)`

`\pm 15-1=y`

`-16,14=y`

The value of y is either -16 or 14.

Therefore the radius of the circle is 17 units. The point (-15,-16) or (-15,14) lies on this circle.