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Thread: Parabola, ellipses, or hyperbolas help!

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    Parabola, ellipses, or hyperbolas help!

    Need help with a problem.

    X^2 + (y+1)^2/3 =1.
    It is x squared plus y+1 squared divided by 3 =1.

    Don't know how to start it. Please help
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    Re: Parabola, ellipses, or hyperbolas help!

    I believe it's an ellipse.
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    Re: Parabola, ellipses, or hyperbolas help!

    Quote Originally Posted by Nfalconer View Post
    Need help with a problem.
    X^2 + (y+1)^2/3 =1.
    It is x squared plus y+1 squared divided by 3 =1.

    Don't know how to start it. Please help
    Is it $x^2+\dfrac{(y+1)^2}{3}=1$ or $\large{x^2+(y+1)^{\frac{2}{3}}=1?}$
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    Re: Parabola, ellipses, or hyperbolas help!

    It is the first one. I am trying to figure out foci and vertices. I know it is a vertical ellipse but that's it. Need to find a b and c.
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    Re: Parabola, ellipses, or hyperbolas help!

    Quote Originally Posted by Nfalconer View Post
    It is the first one. I am trying to figure out foci and vertices. I know it is a vertical ellipse but that's it. Need to find a b and c.
    Do you see how you could have avoided that confusion?

    Write as $x^2+\frac{(y+1)^2}{3}=1$.

    The center of the ellipse is $(0,-1)$.

    The foci are equally distance on each side of the center on the major axis.
    What is the major axis?
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    Re: Parabola, ellipses, or hyperbolas help!

    I got foci 1 as (0,.4) and foci 2 as ( 0, -2.4)
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    Re: Parabola, ellipses, or hyperbolas help!

    For the vertices I got (0,.7) and (0,-2.7)?
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    Re: Parabola, ellipses, or hyperbolas help!

    Quote Originally Posted by Nfalconer View Post
    I got foci 1 as (0,.4) and foci 2 as ( 0, -2.4)
    How did you get those values?
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    Re: Parabola, ellipses, or hyperbolas help!

    For foci 1 I did (h,k+c) so 0, -1+1.4=(0,.4) and foci 2 I did (h, k-c)= (0, -1-1.4)= (0,-2.4). Is that wrong?
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    Re: Parabola, ellipses, or hyperbolas help!

    And the vertices I did (0, -1+1.7) and (0,-1.7+-2)
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    Re: Parabola, ellipses, or hyperbolas help!

    Quote Originally Posted by Nfalconer View Post
    And the vertices I did (0, -1+1.7) and (0,-1.7+-2)
    Tell us how you got $c$. Be detailed, please.
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    Re: Parabola, ellipses, or hyperbolas help!

    I got c by doing 3-1=2 then got +or- 1.4
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    Re: Parabola, ellipses, or hyperbolas help!

    I did A(3) - B(1) to get 2
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    Re: Parabola, ellipses, or hyperbolas help!

    I messed up everything didn't I?
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    Re: Parabola, ellipses, or hyperbolas help!

    Quote Originally Posted by Nfalconer View Post
    And the vertices I did (0, -1+1.7) and (0,-1.7+-2)
    I'm going to slip this in here: It is better to give exact values rather than use decimals. ie. $\displaystyle ( 0, ~ -1 + \sqrt{3} ); ( 0, -1 - \sqrt{3} )$

    -Dan
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