How the coefficient and constant change from a conic section that reflect with a line $x=3$? Where its coefficient and constant are integer.

Question

Let M is a conic section with general equation $Ax^2+Bxy+Cy^2+Dx+Ey=F$ and assume all of the coefficient (A,B,C,D and E) and constant (F) are integer.

When the conic section M reflect on a line $x=3$, please explain :

1. What coefficient that change ? Is it D and E ?
2. Is the constant F also changing ?
3. How much the change of the coefficient D and E ?
4. How much the change of the constant F ?

Thank you for your explaination.

Answer 1

HINT:

Reflection around $x=3$ is the same as plugging in $6-x$ instead of $x$. Can you see why? Then just expand everything and find the new coefficients.