Question

The centre, one vertex and one focus of a hyperbola are $(1,-1)$ , $(5,-1)$ , $(6,-1)$.

The equation of its directrix are:

• A. $5x-21=0,5x+11=0$
• B. $5x+4=0,x+1=0$
• C. $5x-7=0,5x-19=0$
• D. $5x-17=0,5x-6=0$

Answer 1

The correct option is A $5x-21=0,5x+11=0$

Centre is $(1,-1)$
Vertex is $(5,-1)$
Focus is $(6,-1)$
Since axis of hyperbola is parallel to x.axis
distance between center and vertex is a $=4$
distance between center and focus is $ae=5$
$\therefore e=\frac{5}{4}$
Now coming to general equation of directrices with centre at $(0,0)$ is $x=\frac{a}{e}$
But in our case center of hyperbola is shifted ie $(1,-1)$
equation of directrices will be $x-1=\frac{a}{e}andx-1=\frac{-a}{e}$
Substitute the value of a and e
We have
$5x-21=0and5x+11=0$