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Question 471188: how do i know if an equation is a circloe, ellipse, parabola, hyperbola, from an equation if it isn't in standard from, for exsample 9y^2+18y=25x^2+216
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! how do i know if an equation is a circloe, ellipse, parabola, hyperbola, from an equation if it isn't in standard from, for example.
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The first step in rewriting an equation into standard form is to complete the square.
Using given equation as an example:
9y^2+18y=25x^2+216
complete the square
9(y^2+2y+1)-25x^2=216+9
9(y+1)^2-25x^2=225
Divide by 225
(y+1)^2/25-25x^2/9=1
This equation is a hyperbola with vertical transverse axis and center at (-1,0)
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Standard form for hyperbola with vertical transverse axis: (y-k)^2/a^2-(x-h)^2/b^2=1
Standard form for hyperbola with horizontal transverse axis: (x-h)^2/a^2-(y-k)^2/b^2=1
For other conics, use the same procedure and recognizing the standard form for each conic.
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