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Thread: Find vertical tangent

  1. #1

    Find vertical tangent

    Find the point(s) on the curve at which the tangent line is(are) vertical given the curve x2+xy+y2​=3

  2. #2
    Elite Member
    Join Date
    Sep 2005
    Posts
    7,294
    Differentiate implicitly:

    [tex]y'=\frac{-(2x+y)}{x+2y}[/tex]

    Now, vertical tangents occur where the slope is undefined. When the denominator is 0.

    Set the denominator equal to 0 and solve for y. Sub this back into the original and solve for the x. y coordinates follow.

  3. #3
    So I set the denominator equal to 0.

    x+2y= 0

    x=-2y
    y=-x/2

    so I plug these two back into the original equation x2+xy+y2=3 to find the x and y points for the tangent points right?
    y

  4. #4
    Senior Member
    Join Date
    Jan 2012
    Posts
    2,343
    Those are not two separate equations. Putting y= -x/2 into [tex]x^2+ xy+ y^2= 3[/tex] gives [tex]x^2- x^2/2+ x^2/4=3x^2/4= 3[/tex]. Solve that for x and then use y= -x/2 to find the corresponding values for y. OR put x= -2y into the equation: [tex]4y^2- 2y^2+ y^2= 3y^2= 3[/tex]. Solve that for y and then use x= -2y to find the correspondinmg values for x.

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