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Question

Consider a hyperbola H:x22y2=4. Let the tangent at a point P(4,6) meet the x-axis at Q and latus rectum at R(x1,y1),x1>0. If F is a focus of H which is nearer to the point P, then the area of ΔQFR is equal to:


A

6-1

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B

46-1

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C

46

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D

76-2

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Solution

The correct option is D

76-2


Explanation for the correct option:

Step 1. Draw the figure according to the question:

As we know, equation of hyperbola is

x24-y22=1

Eccentricity, e=1+b2a2

=32

Focus, Fae,0=F6,0

Step 2. Equation of tangent at P to the hyperbola is 2x-y6=2

tangent meet x-axis at Q1,0

and Latus rectum x=6 at R6,266-1

Area of QFR=126-1×266-1

=76-2

Hence, Option ‘D’ is Correct.


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