A parabola would be given as the following: $y^2=4px$.
1) The question is, one wishes to find each equation for two orthogonal (perpendicular) tangent lines of a parabola.
What would be the equations?
Add: And one wishes to find the locus of the intersecting point of two orthogonal tangent lines. How would one be able to get the locus?
The book I am reading to says that $y=mx+\frac{p}{m}$ can be the equation for a tangent line of a parabola. Is this right?
2) And suppose that there is a point $P(x_0,y_0)$ outside the parabola (this parabola is the aforementioned.). Assume that from the point, two tangent lines can be drawn. For each line, then, there would be points $Q_1(x_1,y_1)$, $Q_2(x_2,y_2)$.
Then why is $y_1y=2p(x+x_1)$ and $y_2y=2p(x+x_2)$?
Edit: I'll add one more question to 1):
Edit: Adding to 1).