QJEEAdv05Maed67: JEE Advanced 2005 Mathematics - Class 12 JEEAdv05Maed67 Solution: If [ 4 a 2 4 a 1 4 b 2 4 b 1 4 c 2 4 c 1 ] [ f ( − 1 ) f ( 1 )…

If $$\left[\begin{array}{ccc}4a^2& 4a& 1\\ 4b^2& 4b& 1\\ 4c^2& 4c& 1\end{array}\right]\left[\begin{array}{c}f\left(-1\right)\\ f\left(1\right)\\ f\left(2\right)\end{array}\right]=\left[\begin{array}{c}3a^2+3a\\ 3b^2+3b\\ 3c^2+3c\end{array}\right],f\left(x\right)$$ is a quadratic
function and its maximum value occurs at a point $V$ . $A$ is a point of intersection of $y=f(x)$ with $x$ -axis and point $B$ is such that chord $AB$ subtends a right angle at $V$ . Find the area enclosed by $f(x)$ and chord $AB$ .