Points that a curve's normal line intersects

[dustbin]

Homework Statement

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?

 

[LCKurtz]

Homework Statement

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?

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.

 

[dustbin]

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

Thanks for you time! I greatly appreciate it.