The discussion revolves around finding the intersection point of the normal line to the curve defined by the equation x² + 2xy - 3y² = 0 at the point (5,5). The participants successfully differentiated the equation to determine the slope at the specified point, leading to the formulation of the tangent and normal lines. A key insight was recognizing that the curve can be factored, simplifying the process of locating the additional intersection point of the normal line with the curve.
PREREQUISITESStudents studying calculus, particularly those focusing on curve analysis and geometric interpretations of derivatives, as well as educators seeking to enhance their teaching strategies in these areas.
dustbin said: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?