Question

A circle is centered at the point (-3, 2) and passes through the point (1, 5). The radius of the circle is ___ units. The point (-7,__ ) lies on this circle.

Answer 1

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.

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

The center is (-3,2) and the point on the circumference is (1,5)

$r=\sqrt{(1--3)^2+(5-2)^2}$

$r=\sqrt{(4)^2+(3)^2}$

$r=\sqrt{16+9}$

$r=\sqrt{25}$

$\therefore r=5$

The radius is 5 units.

The equation of the circle is given by:

$(x--3)^2+(y-2)^2=5^2$

$(x+3)^2+(y-2)^2=25$

When x=-7, we obtain y by substituting into the equation of the circle:

$(-7+3)^2+(y-2)^2=25$

$(-4)^2+(y-2)^2=25$

$16+(y-2)^2=25$

$(y-2)^2=25-16$

$(y-2)^2=9$

$y-2=\pm \sqrt{9}$

$y=2\pm 3$

$y=-1$ or y=5

Therefore (-7,-1) and (-7,5) lies on the circle.