Question

Find the equation of the hyperbola whose vertices are at (0 ± 7) and foci at $$(0,\pm \frac{28}{3})$$ . 

Answer 1

 The Vertices of the hyperbola are $$(0,\pm 7)$$.

∴ $$b=7$$

The foci is $$(0,\pm \frac{28}{3})$$.

∴ $$be=\frac{28}{3}$$

Also,$$a^2=b^2(e^2-1)$$

$$\Rightarrow a^2={\left(\frac{28}{3}\right)}^2-49$$

$$\Rightarrow a^2=\frac{343}{9}$$

Therefore, the equation of the hyperbola is $$-\frac{9x^2}{343}+\frac{y^2}{49}=1$$.