If the normal to the ellipse 3x^2+4y^2=12 at a point P on it is parallel to the line, 2x+y=4 and the tangent to the ellipse at P passes through Q (4 ,4 ) then PQis equal to:

Question

Accepted Answer

Correct answer: A. (a) JEE Main 2019 Slope of tangent on the line 2x+y=4 at point P is 12. Given ellipse is, 3x^2+4y^2=12 ⇒ x^22^2+ y^2 ( 3 )^2=1 Let point P (2 cos ⁡ , 3 sin ⁡ ) ∴ equation of tangent on the ellipse, at P is, x2 cos ⁡ + y 3 sin ⁡ =1 ⇒m_T=- 32 cot ⁡ ∵ both the tangents are parallel ⇒- 32 cot ⁡ = 12 ⇒ tan ⁡ =- 3 ⇒ = - 3 or =2 - 3 Case-1: = 2 3 then point P(-1 , 32) and PQ= 5 52 Case-2: = 2 3, then tangent does not pass through Q (4 ,4 ).

$If the normal to the ellipse 3 x^{2} + 4 y^{2} = 12 at a point P on it is parallel to the line, 2 x + y = 4 and the tangent to the ellipse at P passes through Q (4, 4) then PQ is equal to:$

Solution

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