Question

Tangent at the point $(2\sqrt{2},3)$ to the hyperbola$\frac{x^2}{4}-\frac{y^2}{9}$= 1 meet its asymptotes at A and B, then area of the triangle OAB, O being the origin is

• A. 6 sq. units
• B. 3 sq. units
• C. 12 sq. units
• D. 2 sq. units

Answer 1

The correct option is A 6 sq. units

Since area of the triangle formed by tangent at any point lying on the hyperbola $\frac{x^2}{b^2}-\frac{y^2}{b^2}$= 1 and its asymptotes is always constant and is equal to ab. Therefore, required area is 2 X 3=6 square units.