# Thread: Equation of the normal line

1. ## Equation of the normal line

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,

2. Originally Posted by kristin08
Write an equation of the normal line that is perpendicular to the tangent line to the curve x^2=xy-y^=1 at a point (2,3)

I don't even know how to start this I need step by step help if possible,
fix your equation ... you have two equal signs.

3. Sorry

4. Originally Posted by kristin08
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)
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 ...

$\displaystyle y - 3 = -\frac{4}{7}(x - 2)$