Question

What is the equation of the circle with center (-1,-2) and passes through the point (6,4)?

Which of the following points is also located on the circle?
A. (6,-6)
B. (-10,0)
C. (-6,4)

Answer 1

`(x+1)^2 + (y+2)^2 = 85`

and B

Explanation:

To write the equation of a circle, use the formula
`(x-h)^2+(y-k)^2 = r^2` where the center of the circle is (h, k).

This means the equation is
`(x--1)^2 + (y--2)^2 = r^2 \\\\ (x+1)^2 + (y+2)^2 = r^2`.

Find the radius r by finding the distance between (-1,-2) and (6,4) using the distance formula.

`d = √((6--1)^2 + (4--2)^2) =√((7)^2 + (6)^2) =√(49+36) =√(85)`

Since the radius is √85 and therefore
`r^2 = 85`.

The equation is
`(x+1)^2 + (y+2)^2 = 85`.

To see what other point is on the circle, substitute the (x,y) in the equation.

(-10+1)^2 + (0+2)^2 = 85

81 + 4 = 85

85 = 85

The point (-10,0) is on the circle.