Question

vertices $(\pm 7,0)$
ecentricity$=\frac{4}{3}$, $ac=4$
find eqn of hyperbola

Answer 1

$\to$ As vertices of hyperbola

are at $(\pm a,0)\Rightarrow a=7$

$e=\frac{4}{3}$ and as $e^2=1+\frac{b^2}{a^2}$

$\Rightarrow b^2=a^2(e^2-1)=49(\frac{16}{9}-1)$

$=\frac{49\times 7}{9}\Rightarrow b=\frac{7\sqrt{7}}{3}$

$\Rightarrow E{q}^n:-\frac{x^2}{49}-\frac{y^2}{49\left(\frac{7}{9}\right)}=1$