Write an equation of the normal line that is perpendicular to the tangent line to the curve x^2+xy-y^2=1 at a point (2,3)
I don't even know how to start this I need step by step help if possible,
Write an equation of the normal line that is perpendicular to the tangent line to the curve x^2+xy-y^2=1 at a point (2,3)
I don't even know how to start this I need step by step help if possible,
derivative ...
$\displaystyle 2x + xy' + y - 2yy' = 0$
$\displaystyle xy' - 2yy' = -2x - y$
$\displaystyle y'(x - 2y) = -(2x+y)$
$\displaystyle y' = \frac{2x+y}{2y-x}$
sub in the coordinates $\displaystyle (2,3)$ ...
$\displaystyle y' = \frac{7}{4}$
normal slope is $\displaystyle -\frac{4}{7}$
equation of the normal line is ...
$\displaystyle y - 3 = -\frac{4}{7}(x - 2)$