You can put this solution on YOUR website! what is 36x^2-9y^2=324 in standard form?
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36x^2-9y^2=324
x^2/9-y^2/36=1
This is a hyperbola with standard form, (x-h)^2/a^2-(y-k)^2/b^2=1
(Note: If the minus sign were a plus sign, the equation would be an ellipse.)
In this case, (h,k)=(0,0), so the center is at the origin ((),0).
Since x^2 comes before y^2, it has a horizontal transverse axis.
If y^2 came before x^2, it would have had a vertical transverse axis.
a^2=9
a=3=(distance from center to vertices
b^2=36
b=6
c^2=a^2+b^2
c=sqrt(a^2+b^2)=sqrt(45)=6.7=distance from center to foci.
asymptotes go thru center and have slopes of +and -b/a=+-2
equation of asymptotes: y=+-2x
See graph of hyperbola below:
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y=+-(36(x^2/9-1))^.5
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