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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Ellipse

NTA Abhyas 2020 · Mathematics · Ellipse

The angle between the pair of tangents drawn to the ellipse 3 x ^ 2...

The angle between the pair of tangents drawn to the ellipse 3x2+2y2=53{x}^{2} + 2{y}^{2} = 5 from the point \left(1, 2\right)is \left|\tan^{- 1}\left(\dfrac{12}{\sqrt{\lambda}}\right)\right|, then the value of λ\lambda is

Correct answer

5

Step-by-step solution

Equation of pair of tangents
(3x2+2y2−5)(6)=(3x+4y−5)2\left(3{x}^{2} + 2{y}^{2} - 5\right)\left(6\right) = {\left(3x + 4y - 5\right)}^{2}
9x2−4y2−24xy+30x+40y−55=09{x}^{2} - 4{y}^{2} - 24xy + 30x + 40y - 55 = 0
tanθ=125tan\theta = \dfrac{12}{\sqrt{5}}
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