Question

The equation of the hyperbola of given transverse axis whose vertex bisects the distance between the centre and the focus, is given by

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is A

Let the equation to the hyperbola be $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ …… (i)
Hence, the transverse axis is 2a. If C is the centre, S is the focus and A is the vertex to the hyperbola, then CS = ae
[distance between the centre and the focus]
$\therefore$ $a=\frac{ae}{2}$ or e=2
Again, $b^2=a^2(e^2-1)=a^2(4-1)=3a^2$
On substituting the value of b2 in Equation (i), we get $\frac{x^2}{a^2}-\frac{y^2}{3a^2}=1$
$\Rightarrow$ $3x^2-y^2=3a^2$