Question

What will be the tangent value of acute angle $\theta$ between the two asymptotes of the hyperbola
$\frac{x^2}{49}-\frac{y^2}{25}=1$

• A. $\tan \theta =\frac{35}{12}$
• B. $\tan \theta =\frac{12}{35}$
• C. $\tan \theta =\frac{12}{37}$
• D. $\tan \theta =\frac{35}{12}$

Answer 1

The correct option is D $\tan \theta =\frac{35}{12}$

Given: Equation of hyperbola is $\frac{x^2}{49}-\frac{y^2}{25}=1$

To Find: Value of acute angle $\theta$ between the two asymptotes

Equation of standard hyperbola is $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

On comparing the given hyperbola equation with the standard hyperbola equation, we have $a^2=49,b^2=25$

$a=7,b=5$

Angle between asymptote is given by, $\tan \theta =|\frac{2ab}{a^2-b^2}|$

Substituting the values of $a$ and $b$.
$\tan \theta =|\frac{2\times 7\times 5}{49-25}|$

$\Rightarrow \tan \theta =|\frac{70}{24}|$

$\Rightarrow \tan \theta =\frac{35}{12}$