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Question 1055157: What's the distance between the parabola y = x^2+4 and x = y^2 ?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! What's the distance between the parabola y = x^2+4 and x = y^2 ?
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General points::
Parabola points:: (x, x^2+4)
Parabola points:: (y^2, y)
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distance = sqrt[(x-y)^2 + (x^2+4-y)^2]
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distance = sqrt[x^2 - 2xy + y^2 + (x^2+4)^2 - 2y(x^2+4) + y^2]
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distance = sqrt[x^2 - 2xy + y^2 + x^4 + 8x^2 + 16 - 2x^2y - 8y + y^2]
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distance = sqrt[x^4 + 9x^2 -2xy - 2x^2y + 2y^2 - 2y + 16]
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Cheers,
Stan H.
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