# Thread: Area between 2 curves

1. ## Area between 2 curves

Find the area between the two curves:

$\displaystyle x = y^2 - 6y$

$\displaystyle x = 5y - y^2$

I have no idea where to start...

2. Originally Posted by topher0805
Find the area between the two curves:

$\displaystyle x = y^2 - 6y$

$\displaystyle x = 5y - y^2$

I have no idea where to start...
Draw a picture. Both of them are parabola's on their sides. Complete the suqare in y to put them in standard form.

3. Originally Posted by danny arrigo
Draw a picture. Both of them are parabola's on their sides. Complete the suqare in y to put them in standard form.
I was given a picture (it's a WebAssign question).

How do I complete the square in this case?

4. Originally Posted by topher0805
Find the area between the two curves:

$\displaystyle x = y^2 - 6y$

$\displaystyle x = 5y - y^2$

I have no idea where to start...
$\displaystyle x = y^2 - 6 y + \left(\frac{-6}{2} \right)^2 - \left(\frac{-6}{2} \right)^2$

$\displaystyle x = (y-3)^2 - 9$

standard form

$\displaystyle x + 9 = (y-3)^2$

The vertex is located at $\displaystyle (-9,3)$