Answer:
The radius is 5 units
(-7,-1) and (-7,5) lies on the circle
Step-by-step explanation:
Use the distance formula to find the distance between the center and the given point that gives you the radius.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The center is (-3,2) and the point on the circumference is (1,5)
[tex]r=\sqrt{(1--3)^2+(5-2)^2}[/tex]
[tex]r=\sqrt{(4)^2+(3)^2}[/tex]
[tex]r=\sqrt{16+9}[/tex]
[tex]r=\sqrt{25}[/tex]
[tex]\therefore r=5[/tex]
The radius is 5 units.
The equation of the circle is given by:
[tex](x--3)^2+(y-2)^2=5^2[/tex]
[tex](x+3)^2+(y-2)^2=25[/tex]
When x=-7, we obtain y by substituting into the equation of the circle:
[tex](-7+3)^2+(y-2)^2=25[/tex]
[tex](-4)^2+(y-2)^2=25[/tex]
[tex]16+(y-2)^2=25[/tex]
[tex](y-2)^2=25-16[/tex]
[tex](y-2)^2=9[/tex]
[tex]y-2=\pm \sqrt{9}[/tex]
[tex]y=2\pm 3[/tex]
[tex]y=-1[/tex] or y=5
Therefore (-7,-1) and (-7,5) lies on the circle.
