Question

The equation of the hyperbola whose foci are (6, 5), (-4, 5) and eccentricity is 5/4, is______.

विकल्प

• \[\frac{(x-1)^{2}}{16}-\frac{(y-5)^{2}}{9}=1\]

• \[\frac{x^{2}}{16}-\frac{y^{2}}{9}=1\]

• \[\frac{(x-1)^{2}}{16}+\frac{(y-5)^{2}}{9}=1\]

• None of these

Answer 1

The equation of the hyperbola whose foci are (6, 5), (-4, 5) and eccentricity is 5/4, is \[\frac{(x-1)^{2}}{16}-\frac{(y-5)^{2}}{9}=1\].

Explanation:

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

\[\Rightarrow\quad2ae=10\]

\[\Rightarrow\quad ae=5\quad\Rightarrow\quad a=4\]

\[\mathrm{Now},b^2=a^2(e^2-1)\Rightarrow b=3\]

Hence, the equation of the hyperbola is \[\frac{(x-1)^2}{16}-\frac{(y-5)^2}{9}=1\]