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anonymous

  • one year ago

I don't know how to approach this question, please help! Find the value of the constant c for which the line y=4x+c is a tangent to the curve y^2=4x

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  1. anonymous
    • one year ago
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    This is what I tried but it doesn't seem to be going anywhere.

  2. rock_mit182
    • one year ago
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    @ganeshie8 help us out

  3. ganeshie8
    • one year ago
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    so far so good

  4. ganeshie8
    • one year ago
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    \(16x^2-4x =-8xc-c^2 \) rearrange the equation in standard form \(16x^2+x(8c-4) + c^2 = 0\) For the line to be a tangent, you want the discriminant to be \(0\) : \((8c-4)^2 - 4*16*c^2=0\) solve \(c\)

  5. anonymous
    • one year ago
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    I am a bit confused with how you rearranged it.

  6. anonymous
    • one year ago
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    How did you decide to put those numbers in the brackets?

  7. ganeshie8
    • one year ago
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    I wanted to see a quadratic in \(x\), so arranged it in decreasing exponent of \(x\)

  8. ganeshie8
    • one year ago
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    Notice that the equation is in form \(ax^2+bx+c=0\)

  9. anonymous
    • one year ago
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    Ok, I think I understand better now. So if I started working on it from that last line I would be going in the right direction with it?

  10. ganeshie8
    • one year ago
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    Yes

  11. anonymous
    • one year ago
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    Thank you!

  12. ganeshie8
    • one year ago
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    yw

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spraguer (Moderator)
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