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Ellipse question

2013 · Shift 1 · Q30
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Ellipse question

2013 · Shift 1 · Q30

JEE AdvancedMathematicsEllipseNumerical+4 / −1
A vertical line passing through the point (h,0)(h,0)(h,0) intersects the ellipse x24+y23=1{{{x^2}} \over 4} + {{{y^2}} \over 3} = 14x2​+3y2​=1 at the points PPP and QQQ. Let the tangents to the ellipse at PPP and QQQ meet at the point RRR. If Δ(h)\Delta \left( h \right)Δ(h)=== area of the triangle PQRPQRPQR, Δ1{{\Delta _1}}Δ1​=max⁡1/2≤h≤1Δ(h)= \mathop {\max }\limits_{1/2 \le h \le 1} \Delta \left( h \right)=1/2≤h≤1max​Δ(h) and Δ2{{\Delta _2}}Δ2​=min⁡1/2≤h≤1Δ(h)= \mathop {\min }\limits_{1/2 \le h \le 1} \Delta \left( h \right)=1/2≤h≤1min​Δ(h), then 85Δ1−8Δ2={8 \over {\sqrt 5 }}{\Delta _1} - 8{\Delta _2} =5​8​Δ1​−8Δ2​=
Numerical answer
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