radius of a circle?

Question

find the radius of a circle given by the equation x^2+y^2-2ax-2ay=0
I get a*sqrt2
but my book says sqrt(2*a)
I think it is wrong. what is your verdict?

Answer 1

r = √(a² + a²)
r = √ (2 a² )
r = √2 a
I agree with you.

Answer 2

Let's see. First we'll use completing-the-square on the equation:

x^2 + y^2 - 2ax - 2ay = 0
(x^2 - 2ax) + (y^2 - 2ay) = 0
(x^2 - 2ax + a^2) + (y^2 - 2ay + a^2) = 2a^2
(x - a)^2 + (y - a)^2 = 2a^2

So the radius would be the square root of the right-hand side, a√2. I say the book might be wrong.

Answer 3

Complete the square
(x^2 - 2ax+ a^2)+(y^2 -2ay + a^2)=(a^2 + a^2)
(x - a)^2+(y - a)^2=2a^2

You should recognize this as the equation of a circle centered at (a,a) with r^2=2a^2
or r = a*sqrt(2)

yup, book be wrong.

Answer 4

Via dimensional analysis, sqrt(2*a) is not a length! It MUST be wrong. Perhaps the author meant sqrt(2a^2)?