Question

Find the equation of hyperbola
Whose center is $(1,0)$, focus is $(6,0)$ and the transverse axis is $6$.

Answer 1

$2a=6$ [Given]

$a=3$

$ae=6\Rightarrow e=2$

$b^2=a^2(e^2-1)=9\times 3=27$

$b^2=27$

$e{q}^n$ of Hyperbola

$\frac{(x-1{)}^2}{9}-\frac{(y-0{)}^2}{27}=1$

$\frac{(x-1{)}^2}{9}-\frac{y^2}{27}=1$