Question 197706
I'm assuming you want to graph {{{x^2 - y^2 + 24y=148}}}



{{{x^2 - y^2 + 24y=148}}} Start with the given equation.



{{{x^2 - (y^2 - 24y)=148}}} Factor out the negative from the {{{y^2}}} coefficient



{{{x^2 - (y^2 - 24y+144-144)=148}}} Take half of -24 to get -12. Square it to get 144. Now add AND subtract this value inside the parenthesis.



{{{x^2 - ((y-12)^2-144)=148}}} Factor.



{{{x^2 - (y-12)^2+144=148}}} Distribute



{{{x^2 - (y-12)^2=148-144}}} Subtract 144 from both sides.



{{{x^2 - (y-12)^2=4}}} Combine like terms.



{{{(x^2)/4 - ((y-12)^2)/4 = 1}}} Divide both sides by 4.



{{{(x^2)/2^2 - ((y-12)^2)/2^2 = 1}}} Rewrite 4 as {{{2^2}}}



{{{((x-0)^2)/2^2 - ((y-12)^2)/2^2 = 1}}} Rewrite "x" as "x-0"



Now the equation is of the form {{{(x-h)^2/a^2-(y-k)^2/b^2=1}}} (which is a hyperbola) where h=0, k=12, a=2, and b=2