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Math Help - For what values of a and b is the line 4x + y = b tangent to the parabola y = ax2 wh

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    For what values of a and b is the line 4x + y = b tangent to the parabola y = ax2 wh

    __a=1/2
    __b=-8
    __a=-1/2
    __b=8
    __a=-20
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by plstevens View Post
    __a=1/2
    __b=-8
    __a=-1/2
    __b=8
    __a=-20
    what does wh in your question mean?

    are the list of a's and b's you gave options to choose?
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    the wh, should be when x=4, and the a's and b's are th choices that i was given
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by plstevens View Post
    the wh, should be when x=4, and the a's and b's are th choices that i was given
    Well, given the parabola y = ax^2, what is the equation of the line tangent to it at x = 4?

    The tangent line must pass through the point (4, 16a).

    y^{\prime} = 2ax, so when x = 4 the slope of the tangent line is 2 \cdot a \cdot 4 = 8a.

    So the equation of the line that passes through the point (4, 16a) that has a slope of 8a is:
    y = mx + b

    y = (8a)x + b


    Insert the point (4, 16a) to find b:
    16a = (8a)(4) + b

    b = 16a - 32a = -16a

    So the tangent line is y = (8a)x - (16a) or in the form given in the problem:
    -(8a)x + y = -16a

    Compare this with
    4x + y = b

    What are your values for a and b?

    -Dan
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