1. math

find the equation of straight line paing through (1,-1)and perpendicular to x2 +xy+6y2.

2. Originally Posted by pramod khanal
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.