Question

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

Answer 1

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

Answer 2

Answer:

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

Step-by-step explanation:

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

Distance formula:

$D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Using distance formula we get,

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

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

$r=17$

The radius of the circle is 17 units.

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

$r=\sqrt{(-15-(-7))^2+(y-(-1))^2}$

$17=\sqrt{64+(y+1)^2}$

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.

$\pm \sqrt{225}=(y+1)$

$\pm 15-1=y$

$-16,14=y$

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.