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Step-by-step explanation:
x=ptanθ+qsecθ and y=psecθ+qtanθ
x²=p²tan²θ+2pqtanθsecθ+q²sec²θ
and
y²=p²sec²θ+2pqsecθtanθ+q²tan²θ
∴, x²-y²
=p²tan²θ+2pqtanθsecθ+q²sec²θ-p²sec²θ-2pqtanθsecθ-q²tan²θ
=tan²θ(p²-q²)-sec²θ(p²-q²)
=(p²-q²)(tan²θ-sec²θ)
=(p²-q²).(-1) [∵, tan²θ-sec²θ=-1]
=q²-p² (Proved)
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