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

NTA Abhyas 2020 · Mathematics · Ellipse

The tangents at the extremities of the latus rectum of the ellipse...

The tangents at the extremities of the latus rectum of the ellipse 3x2+4y2=123x^{2} + 4y^{2} = 12 form a rhombus PQRSPQRS. Area (in sq. units) of the rhombus PQRSPQRS outside the ellipse is equal toThe tangents at the extremities of the latus rectum of the ellipse 3x^ 2 + 4y^ 2 = 12 form a rhombus PQRS . Area (in

Options

  1. A8−23π8 - 2\sqrt{3}\pi
  2. B12−23π12 - 2\sqrt{3}\pi
  3. C14−π14 - \pi
  4. D16−23π16 - 2\sqrt{3}\pi

Correct answer

D. 16−23π16 - 2\sqrt{3}\pi

Step-by-step solution

The tangents at the extremities of the latus rectum of the ellipse 3x^ 2 + 4y^ 2 = 12 form a rhombus PQRS . Area (in
One of the end of latus rectum is (1,32)\left(1, \dfrac{3}{2}\right)
Tangent at (1,32)\left(1, \dfrac{3}{2}\right) is~x+2y=4x + 2y = 4
Area of rhombus =4(12⋅4⋅2)=16= 4\left(\dfrac{1}{2} ⋅ 4 ⋅ 2\right) = 16

Hence, the required area =16−23π= 16 - 2\sqrt{3}\pi& sq. units

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