The line x=8 is the directrix of the ellipse E : x^2a^2+ y^2b^2=1 with the corresponding focus (2 ,0 ). If the tangent to E at the point P in the first quadrant passes through the point (0 ,4 3 ) and…

Question

The line x=8 is the directrix of the ellipse E : x^2a^2+ y^2b^2=1 with the corresponding focus (2 ,0 ). If the tangent to E at the point P in the first quadrant passes through the point (0 ,4 3 ) and intersects the x-axis at Q, then (3 PQ )^2 is equal to

Accepted Answer

Correct answer: 39. (39) Solution ae=8 ..................(1) ae=2 ..................(1) 8e= 2e e^2= 14e= 12 a=4 b^2=a^2(1-e^2) =16 ( 34 )=12 x cos 4+ y sin 2 3=1 sin = 12 =30° P (2 3 , 3 ) Q ( 8 3 ,0 ) (3 PQ )^2=39

$The line x = 8 is the directrix of the ellipse E : \frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{b ^{2}} = 1 with the corresponding focus (2, 0) . If the tangent to E at the point P in the first quadrant passes through the point (0, 43) and intersects the x-axis at Q, then (3 PQ)^{2} is equal to$

Solution

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