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

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

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $|cos\ x + sin\ x| + |cos\ x\ -\ sin\ x| = 2\ sin\ x$ ; $x \in [0,2 \pi ]$ , then maximum integral value of $x$ is

Let $A=\{0,3,4,6,7,8,9,10\} \quad$ and $R$ be the relation defined on A such that $R =\{( x , y ) \in A \times A : x - y \quad$ is odd positive integer or $x-y=2\}$. The minimum number of elements that must be added to the relation $R$, so that it is a symmetric relation, is equal to $...........$.

$\int_{}^{} {x{{\cos }^2}} xdx = $

If $f(x)\, = \left| {\,\begin{array}{*{20}{c}}{\sin x}&{\cos x}&{\tan x}\\{{x^3}}&{{x^2}}&x\\{2x}&1&1\end{array}\,} \right|$, then $\mathop {\lim }\limits_{x \to 0} \frac{{f(x)}}{{{x^2}}}$ is

Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated is

The value of $\sum\limits_{k = 1}^\infty {\frac{{3{k^2} + 3k + 1}}{{{{\left( {{k^2} + k} \right)}^3}}}} $ is equal to

Let $P( - 1,\,0),\,$$Q(0,\,0)$ and $R\,(3,\,3\sqrt 3 )$ be three point . The equation of the bisector of the angle $PQR $ is

The locus of the point of intersection of lines $(x + y)t = a$ and $x - y = at$, where $t$ is the parameter, is

Let $\mathrm{Y}=\mathrm{Y}(\mathrm{X})$ be a curve lying in the first quadrant such that the area enclosed by the line $Y-y=Y^{\prime}(x)(X-x)$ and the co-ordinate axes, where $(\mathrm{x}, \mathrm{y})$ is any point on the curve, is always $\frac{-y^2}{2 Y^{\prime}(x)}+1, Y^{\prime}(x) \neq 0$. If $Y(1)=1$, then $12 Y(2)$ equals

Let $r$ be a root of the equation $x^2+2 x+6=0$. The value of $(r+2)(r+3)(r+4)(r+5)$ is equal to