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0 votes
8.0k views
in Mathematics by (24.0k points)

If the tangents at P and Q meet in T, prove that

(1) TP and TQ subtend equal angles at the focus S

(2) ST2 = SP.SQ, and 

(3) the triangles SPT and STQ are similar.

1 Answer

+2 votes
by (34.3k points)
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Best answer

Let P be the point (at2, 2at1), and Q be the point (at22, 2at2), so that T is the point {at1t2, a(t1 + t2)}.

The perpendicular, TU, from T on this straight line

Similarly TU' has the same numerical value.

The angles PST and QST are therefore equal.

and the angles TSP and TSQ are equal, the triangles SPT and STQ are similar, so that

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