So i have this equation $$-\sqrt{C_1-y^2}=x+C_2$$
I want to get rid of radical by squaring both sides, the negative sign in front of the first term will become positive right?
I know this is a silly question but i need to make sure, my background at algebra is terrible.
On
Yes it is, and your question is not very terrible since after your calculation, you will reach weird things.
$$C_1-y^2=(x+C_2)^2$$
You can of course change the subject and get a nice equation.
$$y^2=-(x+C_2)^2+C_1$$
Even though the equation seems nice, we need to remember that criteria from the equations are $C_1-y^2\geq 0$ and $x+C_2\leq 0$ since square root always take positive root, and things inside positive should be positive (I assume you are working with real variables.
So that's it. You can erase the negative sign (by squaring both sides), but the negative sign does play a role when you try to draw the curve out.
Yes, so you have $$C_1-y^2=(x+C_2)^2.$$