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Find the equation of the tangent to circle x² + y² - 6x + 4y - 12 = 0 which is parallel to line 4x +3y +5

  • maths -

    you want a tangent with slope -4/3

    the circle is

    (x-3)^2 + (y+2)^2 = 25
    2(x-3) + 2(y+2)y' = 0
    y' = -(x-3)/(y+2)

    when y' = -4/3, 3x = 4y+17
    this occurs at (7,1) and (-1,-5)

    The tangents are thus

    4x+3y = 6±25

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