## Finding the graph of an equation

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.
Luke53
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### Finding the graph of an equation

How can I graph the following equation?
x^3 * y^2 = x * y^3 + 6
I don't know how to isolate y (to get y as a function of x).
Thanks.
Luke.

nona.m.nona
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### Re: Finding the graph of an equation

How can I graph the following equation?
x^3 * y^2 = x * y^3 + 6
I don't know how to isolate y (to get y as a function of x).
The solution process would likely require the process (rather complex) for finding the roots of cubic polynomials. Are you required to graph this, or are you being asked for solutions, or some other task?

Luke53
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### Re: Finding the graph of an equation

If I could graph this equation, I would be able to see what points (x,y) are on this graph, so then I could derive the slopes of the tangent lines at several of these points. One solution is (2,1) so this surely is one point on the graph and the slope of the tangent line here is -(11/10) (after implicit differentiation). So how can I find other points that are part of this graph if I can't plot it out ? Probably it would be possible to find some points where the tangent lines are horizontal or vertical, but what about other points on this graph?
Luke.

nona.m.nona
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Joined: Sun Dec 14, 2008 11:07 pm
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### Re: Finding the graph of an equation

If I could graph this equation, I would be able to see what points (x,y) are on this graph, so then I could derive the slopes of the tangent lines at several of these points.
You enquired regarding solving the original equation for y in terms of x. Now you mention graphing, differentiating, finding tangent lines, etc. Kindly please furnish the text of the exercise, as this should serve to clarify what is needing to be done. Thank you.

nona.m.nona
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### Re: Finding the graph of an equation

As an aside, further information, including a portion of the graph, may be viewed at the following link:

http://www.wolframalpha.com/input/?i=x^ ... +y^3+%2B+6

This forum's scripting seems to "break" the link, so it may be required that one copy the above and paste the entire line into the browser's location bar.

Luke53
Posts: 54
Joined: Sun Mar 13, 2011 9:46 am
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### Re: Finding the graph of an equation

Thanks for your hint and showing me the solution on the Wolfram website.
Part of the implicit plot is shown there.
This plot is what I was after.
How can I get this same plot on my graphic calculator (if this is possible)?