Answer:
radius of the circle is 5 units.
the circle passes through the points (-7,5) and (-7, -1).
Step-by-step explanation:
The center of the circle is (-3, 2) and it passes through (1,5)
The standard form of a circle is given by
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here, we have
h = -3, k = 2, x= 1, y = 5
Plugging these values, we get
[tex](1+3)^2+(5-2)^2=r^2\\\\r^2=4^2+3^2\\\\r^2=16+9\\\\r^2=25\\\\r-=5[/tex]
Therefore, the radius of the circle is 5 units.
Now, we have been given that
x = -7 and we have to find the value of y.
The equation of circle is
[tex](x+3)^2+(y-2)^2=5^2[/tex]
Plugging, x = -7 and find y
[tex](-7+3)^2+(y-2)^2=25\\\\16+(y-2)^2=25\\\\(y-2)^2=9\\\\y-2=\pm3\\\\y=3+2,y=-3+2\\\\y=5,-1[/tex]
Therefore, the circle passes through the points (-7,5) and (-7, -1).
