How do I graph the equation #16x^2-9y^2+32x+18y-137=0# on a TI-83?

1 Answer

First you would have to complete the square on both variables, x and y:

Group together the x terms and y terms, and move the constant to the other side.
#16(x^2+2x) -9(y^2-2y)=137#

Now, complete the squares. Half of the linear coefficient, square it, add inside the parentheses on the left and multiply by the factored out number before adding to the right.

#16(x^2+2x+1) -9(y^2-2y+1)=137+16-9#

Completed squares are now factorable:


I can already tell by the form of the equation, that the graph will be a hyperbola. Now, when you solve for y = , there will be two parts to graph.
#-9(y-1)^2=144 - 16(x+1)^2#

Divide both sides by 9, and take the square root:

#sqrt((y-1)^2)=sqrt((144 - 16(x+1)^2)/9)#

So y - 1 = #+-sqrt((144 - 16(x+1)^2)/9)#

And last, add 1: y = #1+-sqrt((144 - 16(x+1)^2)/9)#

You will have to type in two separate equations into your calculator! (TI-83 or 84 models)
y1 = the part with the "+" sign
y2 = the part with the "-" sign

In other online applications or in the TI-nspire, you do not have to solve for y = any more. After this step: #16(x+1)^2-9(y-1)^2=144#
just divide both sides by 144 and simplify:
Here is what the TI-nspire looks like now:Graph of an algebra equation.