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.
