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Calculus - Verify?

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Find the slope of the tangent line to the curve (a lemniscate)

2(x^2+y^2)^2 = 25(x^2-y^2)
it is at pt (3,1)

  • Calculus - Verify? -

    :4(x² + y²)(2x + 2y dy/dx) = 25(2x - 2y dy/dx).

    :4[(3)² + (1)²][2(3) + 2(1)dy/dx] = 25[2(3) - 2(1)dy/dx]

    :4[9 + (1)][6 + 2 dy/dx] = 25[6 - 2 dy/dx]

    :4[10][8 dy/dx] = 25[4 dy/dx]

    Divide both sides by 10

    :4[8 dy/dx] = 10[dy/dx]
    :32[dy/dx] = 10 [dy/dx]
    then I got dy/dx = 10/32

  • Calculus - Verify? -

    You messed up near the end

    look at line
    4[9 + (1)][6 + 2 dy/dx] = 25[6 - 2 dy/dx]
    and then
    4[10][8 dy/dx] = 25[4 dy/dx]

    you added "unlike terms" inside the bracket

    should have been
    40[6+2dy/dx] = 25[6-2dy/dx]
    240 + 80dy/dx = 150 - 50dy/dx
    130dy/dx = -90
    dy/dx = -90/130 = -9/13

    the rest is easy.

  • Calculus - Verify? -

    tyvm <3

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