# Level Curves?

1. Jun 8, 2014

### JC3187

Hi guys,

What is the best way to sketch

0 = x2 - 2x + 4y2 And
8 = x2 - 2x + 4y2

?

How do I sketch these two and how do I know they're both ellipses?
Thank you.

2. Jun 8, 2014

### pasmith

Complete the square in $x$: $x^2 - 2ax = (x - a)^2 - a^2$.

3. Jun 8, 2014

### JC3187

Then what do i do?

4. Jun 9, 2014

### CAF123

What is the general equation for an ellipse in Cartesian coordinates? Can you see why completing the square helps?

5. Jun 9, 2014

### HallsofIvy

Staff Emeritus
$$(x- 1)^2+ y^2= x^2- 2x+ 1+ y^2$$
Do you see how that is connected to $$x^2+ 2x+ y^2$$?