Question

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

Answer 1

The radius is 5 units and the point is (-7, 5).

Explanation:

First we find the distance from the point on the circle to the center. This will give us the radius. We use the distance formula, plugging in the coordinates from these two points:

`d=√((y_2-y_1)^2+(x_2-x_1)^2)\\\\=√((2-5)^2+(-3-1)^2)=√((-3)^2+(-4)^2)\\\\=√(9+16)=√(25)=5`

The radius is 5 units.

We will now use the partial point and the center, with the radius, to find the missing coordinate:

`5=√((y-2)^2+(-7--3)^2)\\\\5=√((y-2)^2+(-4)^2)\\\\5=√((y-2)^2+16)`

We will cancel the radical by squaring both sides:

`5^2=(√((y-2)^2+16))^2\\\\25=(y-2)^2+16`

Subtract 16 from each side:

`25-16=(y-2)^2+16-16\\\\9=(y-2)^2`

We will take the square root of each side:

`√(9)=√((y-2)^2)\\\\3=y-2`

Add 2 to each side:

3+2 = y-2+2

5 = y

Answer 2

(-7, -1) i confirmed and the distance between both -7, -1 and 1,5 to center is 5.

So -1 is the answer!