Manipal Entrance Test 2017 Math Paper

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 the equation of asymptotes bx±ay=0
∴ ab±ay=0
⇒ y=±b
Now, point of intersections are (a,b) and (a,−b)
∴ Area of triangle =

1

2

(ab×2)=ab sq unit