Question

# Find the equation of the hyperbola satisfying the give conditions: Vertices $$\displaystyle \left ( \pm 2,0 \right )$$ foci $$\displaystyle \left ( \pm 3,0 \right )$$

Solution

## Vertices $$\displaystyle \left ( \pm 2,0 \right )$$ foci $$\displaystyle \left ( \pm 3,0 \right )$$Clearly the vertices are on the $$x$$-axis.Therefore, the equation of the hyperbola is of the form  $$\displaystyle \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}= 1$$Since the vertices are $$\displaystyle \left ( \pm 2 , 0 \right )$$$$\Rightarrow a = 2$$and  foci are $$\displaystyle \left ( \pm 3, o \right )\Rightarrow ae = 3$$We know that $$\displaystyle b^{2}= a^{2}(e^2-1)=a^2e^2-a^2=9-4=5$$Thus the equation of the hyperbola is $$\displaystyle \frac{x^{2}}{4}-\frac{y^{2}}{5}= 1$$MathematicsNCERTStandard XI

Suggest Corrections

0

Similar questions
View More

Same exercise questions
View More

People also searched for
View More