Question: Consider the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ the area of the triangle fo...

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

Answer 1

Solution

Equation of tangent at (a, 0) is x = a and the point of intersection of x = a and the asymptotes will be obtained by solving x = a and equation of asymptotes bx + ay = 0.

∴ ab ±ay = 0

⇒ y = ±b

Now points of intersection are (a, b) and (a, -b)

∴ area of triangle = $\frac{1}{2}(abx2)\mspace{6mu} = ab$ sq.unit.

Question: Consider the hyperbola \(\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1\) the area of the triangle fo...

Solution