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

The radius is 5 units

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

Explanation:

Use the distance formula to find the distance between the center and the given point that gives you the radius.

`d=√((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=√((1--3)^2+(5-2)^2)`

`r=√((4)^2+(3)^2)`

`r=√(16+9)`

`r=√(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 √(9)`

`y=2\pm 3`

`y=-1` or y=5

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