Question

How long is the common chord of the circles x^2+y^2=4 and x^2+y^2=4x?

Answer 1

\[x^2+y^2=4\]
and
\[x^2+y^2=4x\]

Answer 2

The first circle has radius 2 and centered at the origin.
The second one has radius 2 and centered at the (2,0)

Answer 3

Can you finish it now?

Answer 4

How does \[x^2+y^2=4x\] become \[(x-2)^2+y^2=4?\]

Answer 5

Because it seems like that's what you are implying

Answer 6

yes

Answer 7

Sorry, but can you explain how?

Answer 8

Expand the second equation

Answer 9

I haven't expanded an equation at all since the summer, so I might be wrong but it seems like x^2+y^2=4x isn't expandable...

Answer 10

\[
x^2 + y^2 =4 x\\
x^2 -4 x +y^2=0\\
x^2 -4 x + 4 - 4 + y^2 =0\\
(x-2)^2 +y^2 -4=0\\
(x-2)^2 +y^2 =4\\

\]

Answer 11

This method is called: completing the square.
Is it clear now

Answer 12

Ahh it makes sense now, I should be able to do the rest. Thank you!

Answer 13

YW