Question

Consider the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$, the area of the triangle formed by the asymptotes and the tangent drawn to it at $(a,0)$ is

• A. $\frac{1}{2}ab$
• B. $ab$
• C. $2ab$
• D. $4ab$

Hint:

For hyperbola, area of triangle formed by asymptotes and tangent at vertex is $ab$.

Answer 1

The Correct Option is B

Step 1: Asymptotes: $y = \pm \frac{b}{a}x$. Tangent at $(a,0)$: $x = a$.}
Step 2: Intersection points: $(a, b)$ and $(a, -b)$. Triangle area = $\frac{1}{2} \times (2b) \times a = ab$.}
Step 3: Final Answer: $ab$.}