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:
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula we get,
[tex]r=\sqrt{(8-(-7))^2+(7-(-1))^2}[/tex]
[tex]r=\sqrt{(15)^2+(8)^2}[/tex]
[tex]r=17[/tex]
The radius of the circle is 17 units.
Let the circle passing through the point (-15,y).
[tex]r=\sqrt{(-15-(-7))^2+(y-(-1))^2}[/tex]
[tex]17=\sqrt{64+(y+1)^2}[/tex]
Taking square root both the sides.
[tex]289=64+(y+1)^2[/tex]
[tex]289-64=(y+1)^2[/tex]
[tex]225=(y+1)^2[/tex]
Taking square root both the sides.
[tex]\pm \sqrt{225}=(y+1)[/tex]
[tex]\pm 15-1=y[/tex]
[tex]-16,14=y[/tex]
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.
