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Math Help - when d1+d1=2a, ellipse. what is d1*d2=a^2?

  1. #1
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    when d1+d1=2a, ellipse. what is d1*d2=a^2?

    ok so i was extremely bored in calculus class, and with my previous knowledge of how people made the ellipse and hyperbola equations... i tried to make an equation for this "definition"... and i couldn't do it.

    since my mathematical imagination is limited, i was wondering if anyone knows whether that condition is even possible?

    lemme rummage through my trash, i think i have the equation i ended up with, with center (0,0), foci (c,0) and (-c,0), and points (x,y)...

    starting with:
    <br />
\sqrt{(x-c)^2 + y^2}\sqrt{(x+c)^2 + y^2}=a^2
    i ended up with:
    <br />
a^4-y^4-x^4-c^4 = 2c^2x^2 + 2y^2x^2 + 2c^2y^2
    i couldn't isolate y, or even y^2, so i couldn't punch this into the calculator, so is this graphable?
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  2. #2
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    Quote Originally Posted by Skerven View Post
    ok so i was extremely bored in calculus class, and with my previous knowledge of how people made the ellipse and hyperbola equations... i tried to make an equation for this "definition"... and i couldn't do it.

    since my mathematical imagination is limited, i was wondering if anyone knows whether that condition is even possible?

    lemme rummage through my trash, i think i have the equation i ended up with, with center (0,0), foci (c,0) and (-c,0), and points (x,y)...

    starting with:
    <br />
\sqrt{(x-c)^2 + y^2}\sqrt{(x+c)^2 + y^2}=a^2
    i ended up with:
    <br />
a^4-y^4-x^4-c^4 = 2c^2x^2 + 2y^2x^2 + 2c^2y^2
    i couldn't isolate y, or even y^2, so i couldn't punch this into the calculator, so is this graphable?
    The curve you have discovered is a Cassini Oval. Read this: Cassini Ovals -- from Wolfram MathWorld
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