Question 202346: identify the following conic. that is, is it a circle, parabola, hyperbola, or ellipse? show why. x^2 - 4y^2 - 4x - 24y =48
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! in general, this type of problem require that we complete the square.
Remember,,separate the x^2 and x^1 terms,,,x^2 must have coefficient =1,,take 1/2 od x^1 coefficient,,,and square it for third term.,,,then add compensating term to equation to balance.
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x^2 -4x -4y^2 -24y =48
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{x^2 -4x }-4{y^2 +6y } =48
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{x^2 -4x -4} -4 {y^2 +6y +9} = 48 -4 -36 = 8,,,,,,(-4*9 = -36)
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{ x-2}^2 -4 {y+3}^2 =8
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divide thru by 8
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{(x-2)^2}/8 -{ (y+3)^2}/2 =1
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This is the std form of a hyperbola
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(x-h)^2 /a^2 - (y-k)^2/b^2 =1
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