Question

The equation of the hyperbola whose foci are (6, 5), (–4, 5) and eccentricity is $\frac{5}{4}$, is

• A.
• B.
  
• C.
• D. None of these

Answer 1

The correct option is A

Centre of the hyperbola is the mid-point of the line joining the two foci, therefore the coordinates of the centre are (1, 5) Now, distance between the foci = 10
$\Rightarrow$ 2ae = 10
$\Rightarrow$ ae = 5 $\Rightarrow$ a = 4
Now, $b^2=a^2(e^2-1)\Rightarrow b=3$
Hence, the equation of the hyperbola is
$\frac{(x-1{)}^2}{16}-\frac{(y-5{)}^2}{9}=1$