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

NTA Abhyas 2020 · Mathematics · Ellipse

If a tangent of slope 2 of the ellipse x ^ 2 a ^ 2 + y ^ 2 1 = 1...

If a tangent of slope 22 of the ellipse x2a2+y21=1\dfrac{{x}^{2}}{{a}^{2}} + \dfrac{{y}^{2}}{1} = 1 passes through the point \left(- 2,0\right),thenthevalueof, then the value of{a}^{2} is equal to

Correct answer

3.75

Step-by-step solution

A tangent of slope 22 to the ellipse x2a2+y21=1\dfrac{{x}^{2}}{{a}^{2}} + \dfrac{{y}^{2}}{1} = 1 is
y=2x±4a2+1y = 2x \pm \sqrt{4{a}^{2} + 1}

Since, it passes through \left(- 2,0\right)<br/><br />⇒ 0 = 2\left(- 2\right) \pm \sqrt{4{a}^{2} + 1}<br/><br />⇒ 4{a}^{2} + 1 = 16 ⇒ {a}^{2} = \dfrac{15}{4} = 3.75$

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