4x2−2y2=1
e=1+a2b2=23
∴ Focus F(ae,0)⇒F(6,0)
equation of tangent at P to the hyperbola is
2x−y6=2
tangent meet x-axis at Q(1,0)
& latus rectum x=6 at R(6,62(6−1))
∴ Area of ΔQFR=21(6−1)⋅62(6−1)
=67−2 sq. units
Consider a hyperbola H:x2−2y2=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 (in sq. units) is equal to
Held on 18 Mar 2021 · Verified 6 Jul 2026.
46
6−1
67−2
46−1
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