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

NTA Abhyas 2020 · Mathematics · Ellipse

If (0,3 + 5 ) is a point on the ellipse whose foci are (2,3) and (-...

If (0,3+5)\left(0,3 + \sqrt{5}\right) is a point on the ellipse whose foci are \left(2,3\right) and \left(- 2,3\right), then the length of the semi-major axis is

Correct answer

3

Step-by-step solution

If PP is a point on the ellipse having SS & S′S' as foci, then

PS+PS′=2aPS + P{S}^{′} = 2a
Where 2a=2a = length of the major-axis
⇒22+5+22+5=2a⇒ \sqrt{{2}^{2} + 5} + \sqrt{{2}^{2} + 5} = 2a
⇒a=3⇒ a = 3= semi-major axis

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