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Question

The value(s) of λ for which the line y=2x+λ touches the hyperbola 16x29y2=144is/are:

A
5
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B
-5
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C
25
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D
25
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Solution

The correct option is D 25
The equation of the hyperbola is
16x29y2=144or x29y216=1On comparing with the standard form x2a2 y2b2 = 1, we get:a2=9, b2=16and On comparing y=2x+λ withthe slope form of the tangent y = mx ± a2m2 b2, we getm=2 and a2m2 b2=±λλ2=9(2)216=3616=20λ=±25

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