The eccentricity of the hyperbola 4 x^2 - 9 y^2 = 16, is - Vidyadip

MCQ

The eccentricity of the hyperbola $4{x^2} - 9{y^2} = 16$, is

A
$\frac{8}{3}$
B
$\frac{5}{4}$
✓
$\frac{{\sqrt {13} }}{3}$
D
$\frac{4}{3}$

✓

Answer

Correct option: C.

$\frac{{\sqrt {13} }}{3}$

c
(c) Given equation of hyperbola, $\frac{{{x^2}}}{4} - \frac{{{y^2}}}{{(16/9)}} = 1$,

$a = 2,\,\,b = \frac{4}{3}$.

As we know, ${b^2} = {a^2}({e^2} - 1)$

==>$\frac{{16}}{9} = 4({e^2} - 1)$

==> ${e^2} = \frac{{13}}{9}$,

$\therefore e = \frac{{\sqrt {13} }}{3}$.

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 ${a^2} + {b^2} + {c^2} + ab + bc + ca \leq 0\,\forall a,\,b,\,c\, \in \,R$ , then the value of determinant $\left| {\begin{array}{*{20}{c}}
{{{(a + b + c)}^2}}&{{a^2} + {b^2}}&1 \\
1&{{{(b + c + 2)}^2}}&{{b^2} + {c^2}} \\
{{c^2} + {a^2}}&1&{{{(c + a + 2)}^2}}
\end{array}} \right|$

Let $S=\{1,2,3, \ldots \ldots, n\}$ and $A=\{(a, b) \mid 1 \leq$ $a, b \leq n\}=S \times S$. A subset $B$ of $A$ is said to be a good subset if $(x, x) \in B$ for every $x \in S$. Then, the number of good subsets of $A$ is

Let three vectors $\overrightarrow{ a }=\alpha \hat{ i }+4 \hat{ j }+2 \hat{ k }$, $\overrightarrow{ b }=5 \hat{ i }+3 \hat{ j }+4 \hat{ k }, \overrightarrow{ c }=x \hat{ i }+y \hat{ j }+z \hat{ k }$ from a triangle such that $\overrightarrow{ c }=\overrightarrow{ a }-\overrightarrow{ b }$ and the area of the triangle is $5 \sqrt{6}$. if $\alpha$ is a positive real number, then $|\overrightarrow{ c }|^2$ is $:$

Given $a_1,a_2,a_3.....$ form an increasing geometric progression with common ratio $r$ such that $log_8a_1 + log_8a_2 +.....+ log_8a_{12} = 2014,$ then the number of ordered pairs of integers $(a_1, r)$ is equal to

The complex numbers $z = x + iy$ which satisfy the equation $\left| {\frac{{z - 5i}}{{z + 5i}}} \right| = 1$ lie on

If a circle passes through the point $(0, 0), (a, 0), (0, b)$ then its centre is

$\left| {\,\begin{array}{*{20}{c}}{bc}&{bc' + b'c}&{b'c'}\\{ca}&{ca' + c'a}&{c'a'}\\{ab}&{ab' + a'b}&{a'b'}\end{array}\,} \right|$ is equal to

The remainder when $428^{2024}$ is divided by $21$ is ............

From the origin, chords are drawn to the circle ${(x - 1)^2} + {y^2} = 1$. The locus of mid points of these chords is a

The value of $\mathop {\lim }\limits_{x \to 0} \frac{2}{x}\log (1 + x)$ is equal to