Chord of contact:
Equation of chord of contact can be given by T = 0, where T = 
.
Illustration: From the point O on the circle x2 + y2 = 25, tangents OP and OQ are drawn to ellipse 
Show that the locus of midpoint of the chord PQ describes curve x
.
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Solution: O ≡ (5 cosθ, 5 sinθ)
Suppose R be middle point of PQ. Let R ≡ (h, k) .
Equation of chord of contact PQ is T = 0
i.e. 
Equation of chord PQ having middle point R(h, k) is
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(1) and (2) are the same equations.
Thus locus of (h, k) is 
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