Question

Equation if hyperbola with vertices (-3,0)and(3,0) and latus rectum 4 is

Answer 1

below................ ; )

Answer 2

The equation of hyperbola with vertex and latus rectum is    $\dfrac{x^{2} }{9}$  -  $\dfrac{y^{2} }{12 }$  = 1

Step-by-step explanation:

Given as :

The vertices of hyperbola = ( - 3 , 0 ) ( 3 , 0 )

Latus rectum = 4

According to question

The standard equation of hyperbola $\dfrac{x^{2} }{a^{2} }$  -  $\dfrac{y^{2} }{b^{2} }$  = 1

vertex = ( $\pm$ a , 0 )  = ( $\pm$ 3 , 0 )  

latus rectum = $\dfrac{b^{2} }{a}$ = 4

∵     a = $\pm$ 3

∴    a² = 9

Thus , b² = 4 a

Or,     b² = 4 × 3 = 12

∴     b² = 12

So, The equation of hyperbola = $\dfrac{x^{2} }{9}$  -  $\dfrac{y^{2} }{12 }$  = 1

Hence, The equation of hyperbola with vertex and latus rectum is             $\dfrac{x^{2} }{9}$  -  $\dfrac{y^{2} }{12 }$  = 1    Answer