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Math Help - Graph sketching

  1. #1
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    Graph sketching

    The question is: Sketch 4x^2 + y^2 - 2y = 8 on a clearly labelled diagram, making clear the main relevant features of the graph.

    Can I manipulate it such that it has an equation of an ellipse i.e. x^2/(3/2)^2 + (y-1)^2/3^2 = 1 ?

    Or should I just make y the subject i.e. y = 1 +or- sq root (9-4x^2) then sketch using my GC?

    Both give different sketches so which is the correct method or is there another way to do this question?
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  2. #2
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    Quote Originally Posted by margaritas View Post
    The question is: Sketch 4x^2 + y^2 - 2y = 8 on a clearly labelled diagram, making clear the main relevant features of the graph.

    Can I manipulate it such that it has an equation of an ellipse i.e. x^2/(3/2)^2 + (y-1)^2/3^2 = 1 ?

    Or should I just make y the subject i.e. y = 1 +or- sq root (9-4x^2) then sketch using my GC?

    Both give different sketches so which is the correct method or is there another way to do this question?
    Both methods will work (assuming you've solved the equations correctly; I didn't bother to check). The ellipse form tells you more than just plugging it in on the graphing calculator, though. (Such as the lengths of the axes, the foci, etc.)

    -Dan
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  3. #3
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    Oh ok thanks! Could somebody help check my equations for each of the two methods? 'Cos I don't seem to get the same answer.
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  4. #4
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    Hello, margaritas!

    Sketch 4x^2 + y^2 - 2y \:=\:8
    Complete the square: . 4x^2 + y^2 - 2y + 1 \:=\:8 + 1

    Then we have: . 4x^2 + (y - 1)^2 \:=\:9

    Divide by 9: . \frac{x^2}{\frac{9}{4}} + \frac{(y-1)^2}{9}\:=\:1\quad\Rightarrow\quad \frac{x^2}{\left(\frac{3}{2}\right)^2} + \frac{(y-1)^2}{3^2}\:=\:1<br />


    Solve for y

    We have: . 4x^2 + (y-1)^2\:=\:9\quad\Rightarrow\quad(y-1)^2\:=\:0-4x^2

    . . y - 1\:=\:\pm\sqrt{9 - 4x^2}\quad\Rightarrow\quad y \:=\:1\pm\sqrt{9-4x^2}


    Your work is absolutely correct!

    They should produce the same graph.
    . . You may be entering them into your GC incorrectly.

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  5. #5
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    Oh ok I know why now! Thanks Soroban!
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