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

NTA Abhyas 2020 · Mathematics · Ellipse

If the tangent to the ellipse x^ 2 + 4y^ 2 = 16 at P (4cos θ,2sin...

If the tangent to the ellipse x2+4y2=16x^{2} + 4y^{2} = 16 at P \left(4cos \theta,2sin\theta\right)isalsoanormaltothecircleis also a normal to the circlex^{2} + y^{2} = 8x + 4y,then the sum of all possible values of \theta is equal to \left(\forall\theta \in\left[0, 2\pi\right]\right)

Options

  1. Aπ2\dfrac{\pi}{2}
  2. Bπ4\dfrac{\pi}{4}
  3. C5π2\dfrac{5\pi}{2}
  4. D7π4\dfrac{7\pi}{4}

Correct answer

A. π2\dfrac{\pi}{2}

Step-by-step solution

Tangent to the ellipse is xcosθ+2ysinθ=4xcos \theta + 2ysin \theta = 4 which is a normal to the given circle
⇒⇒ it satisfies~\left(4, 2\right)<br/><br />⇒ sin \theta + cos \theta = 1<br/><br />∴ \theta = 0, \dfrac{\pi}{2}
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