Question

If $(a,a^2)$ falls inside the angle made by the lines $y=\frac{x}{2},x>0$ and $y=3x$, then $a$ belongs to

• A. $\left(3,\infty \right)$
• B. $\left(\frac{1}{2},3\right)$
• C. $\left(-3,-\frac{1}{2}\right)$
• D. $\left(0,-\frac{1}{2}\right)$

Answer 1

Answer: (B)

$\left(\frac{1}{2},3\right)$

Consider the diagram shown below.

Draw a line parallel to $x=0$. Therefore,

Coordinates of $P=(a,3a)$

Coordinates of $Q=(a,\frac{a}{2})$

Therefore, we have

$\Rightarrow \frac{a}{2}<a^2<3a$

$\Rightarrow \frac{1}{2}<a<3$

$\Rightarrow a\in (\frac{1}{2},3)$

Hence, this is the required result.