Question

The centre, one vertex, one focus of a hyperbola are $(5,4)$ , $(5,7)$ , $(5,9)$. Its directrices are

• A. $5y-27=0,5y-9=0$
• B. $5y-17=0,5y-11=0$
• C. $5y-29=0,5y-11=0$
• D. $5y-7=0,5y-17=0$

Answer 1

The correct option is C $5y-29=0,5y-11=0$

$a=3;ae=5$
$\Rightarrow e=\frac{5}{3}$
Equation of directrix is $y=4\pm \frac{a}{e}$
$y=4\pm \frac{3}{\frac{5}{3}}$
$y=4\pm \frac{9}{5}$
$y=\frac{11}{5};y=\frac{29}{5}$