The parabola P:y=ax2, where a is a positive real constant, is touched by the line L:y=mx−b (where m is a positive constant and b is real) at the point T. Let Q be the point of intersection of the line L and y−axis such that TQ=1. If A denotes the maximum value of the region surrounded by P, L and the x−axis, then the value of 1A is

The parabola P:y=ax2, where a is a positive real constant, is touched

1.	The parabola P:y=ax2, where a is a positive real constant, is touched by the line L:y=mx−b (where m is a positive constant and b is real) at the point T. Let Q be the point of intersection of the line L and y−axis such that TQ=1. If A denotes the maximum value of the region surrounded by P, L and the x−axis, then the value of 1A is
Answer» The parabola $P : y = a x^{2},$ where $a$ is a positive real constant, is touched by the line $L : y = m x - b$ (where $m$ is a positive constant and $b$ is real) at the point $T .$ Let $Q$ be the point of intersection of the line $L$ and $y -$ axis such that $T Q = 1.$ If $A$ denotes the maximum value of the region surrounded by $P,$ $L$ and the $x -$ axis, then the value of $\frac{1}{A}$ is