If the line y = 2x + be a tangent to the hyperbola 36 x^2 - 25 y^… - Vidyadip

MCQ

If the line $y = 2x + \lambda $ be a tangent to the hyperbola $36{x^2} - 25{y^2} = 3600$, then $\lambda = $

A
$16$
B
$-16$
✓
$ \pm 16$
D
None of these

✓

Answer

Correct option: C.

$ \pm 16$

c
(c) If $y = 2x + \lambda $ is tangent to given hyperabola,

then $\lambda = \pm \sqrt {{a^2}{m^2} - {b^2}} = \pm \sqrt {(100)\,(4) - 144}$

$= \pm \sqrt {256} = \pm 16$.

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