# Points that a curve's normal line intersects

1. Jun 28, 2012

### dustbin

1. The problem statement, all variables and given/known data

The line that is normal to the curve x2+2xy-3y2=0 at (5,5) intersects the curve at what other point?

2. The attempt at a solution

I differentiated the equation, found the slope of the curve at that point, and I then found the equations for the tangent line and normal line. I'm not really sure where to approach from here... any hints?

2. Jun 28, 2012

### LCKurtz

Have you noticed that $x^2+2xy-3y^2\$factors? What does its graph look like? Finding where that normal line hits it again won't seem so difficult.

3. Jun 29, 2012

### dustbin

D'oh! I was looking way too hard. I can't believe I missed that.

Thanks for you time! I greatly appreciate it.