The distance between the foci of a hyperbola is 16 and its eccent… - Vidyadip

MCQ

The distance between the foci of a hyperbola is 16 and its eccentricity is $\sqrt2$ , then equation of the hyperbola is

A
$x^2+y^2=32$
B
$x^2-y^2=16$
C
$x^2+y^2=16$
✓
$x^2-y^2=32$

✓

Answer

Correct option: D.

$x^2-y^2=32$

$x^2-y^2=32$

Solution:
The distance between the foci is 2ae.
$\therefore$ 2ae = 16
⇒ ae = 8
$\text{e}=\sqrt2$
$\therefore\text{a}\sqrt2=8$
$\Rightarrow\text{a}=4\sqrt2$
Also, $b^2 = a^2(e^2 − 1)$
$\Rightarrow b^2 = 32(2 − 1)$
$\Rightarrow b^2 = 32$
Standard form of the hyperbola is given below:
$\frac{\text{x}^2}{32}-\frac{\text{y}^2}{32}=1$
$\text{x}^2-\text{y}^2=32$

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