Q

# Find the equations of the hyperbola satisfying the given conditions.Vertices (± 2, 0), foci (± 3, 0)

7. Find the equations of the hyperbola satisfying the given conditions.

Vertices (± 2, 0), foci (± 3, 0)

Views

Given, in a hyperbola

Vertices (± 2, 0), foci (± 3, 0)

Here, Vertices and focii are on the X-axis so, the standard equation of the Hyperbola will be ;

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

By comparing the standard parameter (Vertices and foci) with the given one, we get

$a=2$ and $c=3$

Now, As we know the relation  in a hyperbola

$c^2=a^2+b^2$

$b^2=c^2-a^2$

$b^2=3^2-2^2$

$b^2=9-4=5$

Hence,The Equation of the hyperbola is ;

$\frac{x^2}{4}-\frac{y^2}{5}=1$

Exams
Articles
Questions