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Math Help - how do i find an equation for the hyperbola with the given information

  1. #1
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    Angry how do i find an equation for the hyperbola with the given information

    i have absolutely no clue how to figure this one out

    focus at (-4,0); vertices at (-4,4) and (-4,2)
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  2. #2
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    Re: how do i find an equation for the hyperbola with the given information

    Quote Originally Posted by alyse2526 View Post
    i have absolutely no clue how to figure this one out

    focus at (-4,0); vertices at (-4,4) and (-4,2)
    1. Draw a sketch.

    2. Determine the coordinates of the midpoint of the hyperbola. (M(x_M , y_M))

    3. Determine the value of the excentricity e (that's the distance between the midpoint and one focus)

    4. Determine the length of the axis a (that's the distance between the midpoint and one vertex)

    5. Calculate the length of the axis b using e^2=a^2+b^2

    6. Use the equation

    \frac{(x-x_M)^2}{a^2} - \frac{(y-y_M)^2}{b^2}=1
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