A hyperbola whose transverse axis is along th | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

$\left( c \right)\,\,\,\,\frac{{{x^2}}}{{12}} + \frac{{{y^2}}}{{16}} = 1$

$e = \sqrt {1 - \frac{{12}}{{16}}}  = \frac{1}{2}$

Foci $(0,2)$ &

Vedclass · Accepted Answer

$\left( {5,2\sqrt 3 } \right)$

Vedclass · Answer

$\left( c ight)\,\,\,\,\frac{{{x^2}}}{{12}} + \frac{{{y^2}}}{{16}} = 1$

$e = \sqrt {1 - \frac{{12}}{{16}}}  = \frac{1}{2}$

Foci $(0,2)$ &$(0,-2)$

So, transverse axis of hyperbola $a = 2b = 4 \Rightarrow b = 2$

 ${a^2} = {1^2}\left( {{e^2} - 1} ight)$

$ \Rightarrow {a^2} = 4\left( {\frac{9}{4} - 1} ight)$

$ \Rightarrow {a^2} = 5$

$	herefore $ It's equation is $\frac{{{x^2}}}{5} + \frac{{{y^2}}}{4} = 1$

The point $\left( {5,2\sqrt 3 } ight)$does not satisfy the above equation.

A hyperbola whose transverse axis is along the major axis of then conic, $\frac{{{x^2}}}{3} + \frac{{{y^2}}}{4} = 4$ and has vertices at the foci of this conic . If the eccentricity of the hyperbola is $\frac{3}{2}$ , then which of the following points does $NOT$ lie on it ?

Similar Questions

Let $A$ be a point on the $x$-axis. Common tangents are drawn from $A$ to the curves $x^2+y^2=8$ and $y^2= 16x.$ If one of these tangents touches the two curves at $Q$ and $R$, then $( QR )^2$ is equal to

The product of the lengths of perpendiculars drawn from any point on the hyperbola ${x^2} - 2{y^2} - 2 = 0$ to its asymptotes is

Eccentricity of the rectangular hyperbola $\int_0^1 {{e^x}\left( {\frac{1}{x} - \frac{1}{{{x^3}}}} \right)} \;dx$ is

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola $\frac{y^{2}}{9}-\frac{x^{2}}{27}=1$

If the line $y=m x+c$ is a common tangent to the hyperbola $\frac{x^{2}}{100}-\frac{y^{2}}{64}=1$ and the circle $x^{2}+y^{2}=36,$ then which one of the following is true?