SOLUTION: My problem is I have the equation: x^2 - y^2 + 24y > (or equal to) 148 Well I put it in graphing form which I believe is (x^2)/292 - (y^2+12)/292=1 Which makes it a Hyperbola, an

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: My problem is I have the equation: x^2 - y^2 + 24y > (or equal to) 148 Well I put it in graphing form which I believe is (x^2)/292 - (y^2+12)/292=1 Which makes it a Hyperbola, an      Log On


   

Question 197706: My problem is I have the equation: x^2 - y^2 + 24y > (or equal to) 148
Well I put it in graphing form which I believe is (x^2)/292 - (y^2+12)/292=1
Which makes it a Hyperbola, and I need to graph it but the radius is the square root of 292, which is 17.08800749, and that is too big to be graphed on my paper and that can't happen because it has to fit. So what did I do wrong? Could you tell me the correct equation and the vertical and horizontal radius?
I did not receive this question from a textbook.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to graph x%5E2+-+y%5E2+%2B+24y=148


x%5E2+-+y%5E2+%2B+24y=148 Start with the given equation.


x%5E2+-+%28y%5E2+-+24y%29=148 Factor out the negative from the y%5E2 coefficient


x%5E2+-+%28y%5E2+-+24y%2B144-144%29=148 Take half of -24 to get -12. Square it to get 144. Now add AND subtract this value inside the parenthesis.


x%5E2+-+%28%28y-12%29%5E2-144%29=148 Factor.


x%5E2+-+%28y-12%29%5E2%2B144=148 Distribute


x%5E2+-+%28y-12%29%5E2=148-144 Subtract 144 from both sides.


x%5E2+-+%28y-12%29%5E2=4 Combine like terms.


%28x%5E2%29%2F4+-+%28%28y-12%29%5E2%29%2F4+=+1 Divide both sides by 4.


%28x%5E2%29%2F2%5E2+-+%28%28y-12%29%5E2%29%2F2%5E2+=+1 Rewrite 4 as 2%5E2


%28%28x-0%29%5E2%29%2F2%5E2+-+%28%28y-12%29%5E2%29%2F2%5E2+=+1 Rewrite "x" as "x-0"


Now the equation is of the form %28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1 (which is a hyperbola) where h=0, k=12, a=2, and b=2