The distance between the directrices of the hyperbola x2-y2 =9 is

Question

The distance between the directrices of the hyperbola x2-y2 =9 is (A) (9/√2) (B) (5/√3) (C) (3/√2) (D) 3√2

Tardigrade Admin · Accepted Answer

Distance between the directrices =(2 a/e) Now, equation of hyperbola is x2-y2=9 It is a rectangular hyperbola and its eccentricity is always √2. ∴ Required distance =(2 × 3/√2)=3 √2

Q. The distance between the directrices of the hyperbola $x^{2} - y^{2} = 9$ is

$\frac{9}{2}$

$\frac{5}{3}$

$\frac{3}{2}$

$32$

$53$

Distance between the directrices
$= \frac{2 a}{e}$
Now, equation of hyperbola is
$x^{2} - y^{2} = 9$
It is a rectangular hyperbola and its eccentricity is always $2$ .
$∴$ Required distance
$= \frac{2 \times 3}{2} = 32$

Q. The distance between the directrices of the hyperbola x2−y2=9 is

2​9​

3​5​

2​3​

32​

53​

Distance between the directrices =e2a​ Now, equation of hyperbola is x2−y2=9 It is a rectangular hyperbola and its eccentricity is always 2​. ∴ Required distance =2​2×3​=32​