How do you graph #x^2-4(y+6)^2 = 9#?

1 Answer
Tony B
Dec 21, 2016

#color(purple)("Note that graphing and sketching are two different things")#
#color(purple)("To sketch a curve you have to mathematically determine important points")#
Depends on what medium you use to plot it. A bit of specialist software could do so by entering the equation as presented.

However, if you wish to do this by hand from a table of values you need to manipulate the equation to give you the format of #y="something"#
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#4(y+6)^2=x^2-9#

#(y+6)^2=1/4x^2-9/4#

#y+6=+-sqrt(x^2-9)/2#

#y=+-sqrt(x^2-9)/2 -6#
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#color(red)("Split equation" -> y=+-(sqrt(x^2-9))/2-6)#
Tony B
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(red)("Full equation" -> x^2-4(y+6)^2=9)#
Tony B

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