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    Consider the quartic equation \displaystyle Ax^2 + Cy^2 + Dx + Ey + F = 0

    If AC> 0 show that it leads to an ellipse.

    RIght, if AC > 0, it imples (A and C) < 0 OR (A and C) > 0. After completing the square etc I managed to get an equation of an ellipse but, when I plugged in values for A and C in graphmatica, I found that if (A and C) > 0 (positive values) the graph could not be plotted. Can someone please explain this to me?
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    (Original post by andrewlee89)
    Consider the quartic equation \displaystyle Ax^2 + Cy^2 + Dx + Ey + F = 0

    If AC> 0 show that it leads to an ellipse.

    RIght, if AC > 0, it imples (A and C) < 0 OR (A and C) > 0. After completing the square etc I managed to get an equation of an ellipse but, when I plugged in values for A and C in graphmatica, I found that if (A and C) > 0 (positive values) the graph could not be plotted. Can someone please explain this to me?
    I'm afraid you are wrong.

    If A=1, C=2, D=0, E=0, F=-1 you have an ellipse and A and C are both positive so this condition is not preventing the graph from being plotted.

    And it isn't a quartic equation.
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    how is x^2 + 2y^2 = 0 an ellipse?
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    Anything in the form ax^2 + by^2 + cy + dx = z is an ellipse unless a = b, in which case you have the special case. The special case is a circle.
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    (Original post by andrewlee89)
    how is x^2 + 2y^2 = 0 an ellipse?
    Ok, I modified my previous result to make you feel happier! Your reasoning was incorrect in any event.
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    yea well im sorry i got it wrong lol! is the circle the only special case?
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    (Original post by Mr M)
    Ok, I modified my previous result to make you feel happier! Your reasoning was incorrect in any event.
    I've gotanother ellipse question, if a standard ellipse (X/a)^2+(Y/B)^2=1 and is shifted to (h,0) what is the new equation foci and directrices so far I have (x-H/a)^2 + (y/B)^2=1 for the equation is that right? From then on im completely stuck any ideas
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    That should be (x/a - h)^2 + (y/b)^2 = 1
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    (Original post by Davidosh)
    I've gotanother ellipse question, if a standard ellipse (X/a)^2+(Y/B)^2=1 and is shifted to (h,0) what is the new equation foci and directrices so far I have ((x-h)/a)^2 + (y/B)^2=1 for the equation is that right? From then on im completely stuck any ideas
    Hancock's answer was incorrect. Yours was correct (assuming you had a bracket where I added it).

    You also need to translate the foci and directices in exactly the same way.

    The bottom example on this page will help.

    http://www.valleyview.k12.oh.us/vvhs...ipseguide.html
 
 
 
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