Question

Which of the following is a degenerate circle?

x^2 + y^2 = 1
x+y = 2
x^2+y^2=-1
(x-4)^2 + (y-2)^2 = 0

Answer 1

The answer is (x-4)^2 + (y-2)^2 = 0

Explanation:

I just took the test and it was right.

Answer 2

Explanation:

Alright, lets get started.

The standard equation of a circle is :

`(x-a)^2+(y-b)^2=r^2`

Where (a,b) are center of circle and r is the radius of circle.

The first given equation is of only this format.

The first equation is :
`x^2+y^2=1`

It means the center (a,b) is equal to (0,0) and radius will equal to 1.

Second,
`x+y=2` is the equation of line.

Third ,
`x^2+y^2=-1` the radius can not be negative.

Fourth,
`(x-4)^2+(y-2)^2=0` the radius can not be zero.

Hence the only equation that degenerate circle is
`x^2+y^2=1` : Answer

Hope it will help :)