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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).

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    For the equations in your second question, what are "$x$" and "$y$", and where are "$x_0$" and "$y_0$"?2012-10-14

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