# Homework Help: Is there a transformation if at all?

1. Aug 31, 2011

### flyingpig

1. The problem statement, all variables and given/known data

Consider

Ax2 + Bxy + Cy2 + Dx + Ey = F

What happens if

Ax2 + B(x + h)(y + k) + Cy2 + Dx + Ey = F

3. The attempt at a solution

Does it do anything?

2. Aug 31, 2011

### Staff: Mentor

I'll say yes, but I wouldn't say this is any kind of normal transformation, since you are replacing only some x and y values by x + h and y + k.

3. Aug 31, 2011

### vela

Staff Emeritus
Multiply it out and write it in the form

A'x2 + B'xy + C'y2 + D'x + E'y = F'

That should shed some light on the effect of modifying the cross term.

4. Aug 31, 2011

### SammyS

Staff Emeritus
If what you say is taken literally, it means that

xy = (x + h)(y + k) .

5. Sep 3, 2011

### flyingpig

@Sammy

Only if h and k are 0.

@vela, I would but I am moving back to the college and i packed everything and it looked a little tedious. I will get back to that diff and continu thread when I got my stuff set.

Also this is jsut a "theory" before application. I am just gonna guess that B(h + k) will get absorbed into the F

So that B(h + k) + F = K?
And so do the other terms get abosrbed.

6. Sep 5, 2011

### SammyS

Staff Emeritus
So, that means that A, B, C, D, E, F do not represent the same set of numbers in the first equation compared to the second equation.

So, you should use primes or subscripts or some such scheme to differentiate (not in the Calculus sense) the two cases.