Question

Area of the triangle formed by any tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ with its asymptotes is

• A. $ab$
• B. $abc$
• C. $4ab$
• D. $a^2{b}^2$

Answer 1

The correct option is A $ab$

suppose the tangent is at $(a,o)$ parallel to y-axis then

then, $A(0,0)B(a,b)C(a,-b)$

$BC=2b$

height $=a$

Area $=\frac{1}{2}base\times height=\frac{1}{2}\times 2b\times a=ab$

A is correct.