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

NTA Abhyas 2020 · Mathematics · Ellipse

The ellipse E _ 1 : x ^ 2 9 + y ^ 2 4 = 1 is inscribed in a...

The ellipse E1:x29+y24=1{E}_{1}: \dfrac{{x}^{2}}{9} + \dfrac{{y}^{2}}{4} = 1 is inscribed in a rectangle RR whose sides are parallel to the coordinate axes. Another ellipse E2{E}_{2} passing through the point (0,4)\left(0, 4\right) circumscribes the rectangle RR. The length (in units) of the major axis of ellipse E2{E}_{2} isThe ellipse E _ 1 : x ^ 2 9 + y ^ 2 4 = 1 is inscribed in a rectangle R whose sides are parallel to the coordinate

Correct answer

8

Step-by-step solution

Let the ellipse be x2a2+y2b2=1\dfrac{{x}^{2}}{{a}^{2}} + \dfrac{{y}^{2}}{{b}^{2}} = 1
The ellipse E _ 1 : x ^ 2 9 + y ^ 2 4 = 1 is inscribed in a rectangle R whose sides are parallel to the coordinate
As it is passing through (0,4)and(3,2)\left(0, 4\right) and \left(3, 2\right). So, {b}^{2} = 16 and 9a2+416=1\dfrac{9}{{a}^{2}} + \dfrac{4}{16} = 1 or {a}^{2} = 12
So, the length of major axis =2b=8= 2b = 8
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