i have the eqautions
5x^2 + 9y^2=45
16x^2-4y^2+64=0
how do i make these into the hyperbola and ellipse form
They are already in "hyerbola and ellipse form". What you mean is into "standard form".
Standard form for an ellipse is
and you have . Divide both sides by 45 to get "1" on the right.
Standard form for an ellipse is either or . You have which is the same as . (We cannot divide "0" by anything to get "1" so I subtracted 64 from both sides.) Divide both sides by -64 to get "1" on the right.