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Math Help - Find the equation of both lines?

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    Find the equation of both lines?

    Determine the equation of both lines that are tangent to the graph of y=x^2 +4 and pass through the point (1,-2)

    So would I simply use the y=mx+b form, m=2, y= -2, and x = 1?
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  2. #2
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    Quote Originally Posted by RyGuy View Post
    Determine the equation of both lines that are tangent to the graph of y=x^2 +4 and pass through the point (1,-2)

    So would I simply use the y=mx+b form, m=2, y= -2, and x = 1?
    no ... the point (1,-2) does not lie on the parabola.
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    Quote Originally Posted by skeeter View Post
    no ... the point (1,-2) does not lie on the parabola.
    Oh right.

    So then how would I go about this?
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    Quote Originally Posted by RyGuy View Post
    Determine the equation of both lines that are tangent to the graph of y=x^2 +4 and pass through the point (1,-2)

    So would I simply use the y=mx+b form, m=2, y= -2, and x = 1?
    the derivative of the parabola equation gives the slope of all tangent lines to the curve.

    You need the equations of the two that pass through (1,-2).

    hence, write the derivative to get the slopes of these lines.
    then use

    y-y_1=m(x-x_1)
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  5. #5
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    point of tangency on the curve is (x,x^2+4)<br />

    each tangent line passes thru the point (1, -2)

    remember how to find the slope between two points?

    ... also, note that the slope of both tangent lines is y' = 2x

    I'll let you take it from here.
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