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  1. #1
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    Smile math

    find the equation of straight line paing through (1,-1)and perpendicular to x2 +xy+6y2.
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    Quote Originally Posted by pramod khanal View Post
    find the equation of straight line paing through (1,-1)and perpendicular to x2 +xy+6y2.
    Hello,

    1. I assume that the equation of the curve reads:

    x^2+xy+6y^2=6 The curve is an ellipse which contains the point A(1, -1).

    2. Use implicite deifferentiation to get the gradient at A:

    2x+(y+x \cdot y') +12y \cdot y'=0 . Plug in the values for x and y and solve the equation for y': I've got y'=\frac1{11}

    The direction perpendicular to y' has the slope m = -11. Use the point-slope-formula to calculate the equation of the line:

    \frac{y-(-1)}{x-1}=-11~\iff~\boxed{y=-11x + 10}

    I've attached a sketch of the situation.
    Attached Thumbnails Attached Thumbnails math-senkr_auf_ellipse.gif  
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