Jee Main Jan 30 Shift 1 Mathematics - Question4
Question 4
The value of maximum area possible of a $\triangle A B C$ such that $A(0,0)$ and $B(x, y)$ and $C(-x, y)$ such that $y=-2 x^{2}+54 x$ is (in sq. unit)
(1) 5800
(2) 5832
(3) 5942
(4) 6008
Show Answer
Answer: (2)
Solution:
Area of $\Delta$
$=\frac{1}{2}\left|\begin{array}{ccc}0 & 0 & 1 \\ x & y & 1 \\ -x & y & 1\end{array}\right|$
$\Rightarrow\left|\frac{1}{2}(x y+x y)\right|=|x y|$
Area $(\Delta)=|x y|=\left|x\left(-2 x^{2}+54 x\right)\right|$
$\frac{d(\Delta)}{d x}=\left|\left(-6 x^{2}+108 x\right)\right| \Rightarrow \frac{d \Delta}{d x}=0$ at $x=0$ and 18
$\Rightarrow$ at $x=0$, minima
and at $x=18$ maxima
Area $(\Delta)=\left|18\left(-2(18)^{2}+54 \times 18\right)\right|=5832$
BETA
