Question

If (−4, 11) and (−6, 5) are the endpoints of a diameter of a circle, what is the equation of the circle?

A) (x + 5)^2 + (y − 8)^2 = 100
B) (x + 5)^2 + (y − 8)^2 = 10
C) (x − 5)^2 − (y + 8)^2 = 10
D) (x − 5)^2 + (y + 10)^2 = 8

Answer 1

A.
`(x+5)^2+(y-8)^2=100`

Explanation:

1. The standard form of the equation of a circle is
`(x-h)^(2) + (y-k)^2=r^2`

2. To find the center we require the midpoint of the 2 given points

center =
`[(1)/(2)(-4-6),(1)/(2)(11+5)]`

=(-5,8)

3. The radius is the distance from the centre to either of the 2 given points calculate the radius using the distance formula

d=
`\sqrt{(x_(2)+x_(1))^(2) +(y_(2)-y_(1))^(2)`

let
`(x_(1),y_(1))= (-5,8) \\` and
`(x_2,y_2)=(-4,11)`

r=
`√((-4+5)^2+(11-8)^2) =√(81+9)=10`

-->
`(x-(-5)^2+(y-8)^2=10^2`

-->
`(x+5)^2+(y-8)^2=100`

Answer 2

The anser is B 100% willing to put $100 on it.

Explanation: