Discussion Forum



1)

 If the lengths of the transverse axis and the latus rectum of a hyperbola are 6 and $\frac{8}{3}$ respectively, then the equation of the hyperbola is ....


A) $4x^{2}-9y^{2}=72$

B) $4x^{2}-9y^{2}=36$

C) $9x^{2}-4y^{2}=72$

D) $9x^{2}-4y^{2}=6$

Answer:

Option B

Explanation:

 we have,

 Length of transverse axis 2a=6$\Rightarrow$  a=3

 and length of  latusrectum,  $\frac{2b^{2}}{a}=\frac{8}{3}$

 $\Rightarrow 2b^{2}=\frac{8}{3}\times3=8\Rightarrow b^{2}=4 $

 $\therefore$  Required equation  of hyperbola is 

$\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\Rightarrow \frac{x^{2}}{9}-\frac{y^{2}}{4}=1\Rightarrow 4x^{2}-9y^{2}=36$