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Question

A straight line is drawn parallel to the conjugate axis of the hyperbola x2a2y2b2=1 to meet it and the conjugate hyperbola respectively in the point P and Q. The normals at p and Q to the curves meet on

A
xaxis
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B
yaxis
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C
y=x
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D
y=x
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Solution

The correct option is A xaxis
Equation of hyperbola x292y262=1
Conjugate hyperbola y262x292=1
Line || to conjugate axis of hyperbola (yaxis) is drawn to meet conjugate axis at P & Q which are symmetric points about xaxis then
P(atanθ,bsintheta)
Q(atanθ,bsinθ)
Normal at Paxtanθ+6ysecθ=a2+b2
Normal at Qaxtanθ6ysecθ=a2+b2
Let us find out interrection
bsecθ=6ysecθ
y=0
9+ lies on xaxis
A is correct


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