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anonymous

  • one year ago

If the equation of an ellipse is in standard form and the denominators are equal, then the ellipse is a circle. Is this true or false?

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  1. phi
    • one year ago
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    do you know the equation of a circle? Start with the equation of an ellipse: \[ \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2 } = 1 \] make the denominators equal. OK, let b = a so we have \[ \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{a^2 } = 1 \] or \[ \frac{(x-h)^2+(y-k)^2}{a^2} =1 \] if you multiply both sides by a^2 you get \[ (x-h)^2+(y-k)^2 = a^2 \]

  2. anonymous
    • one year ago
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    Thank you!

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