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

Question

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

Dr. Abubacker · Accepted Answer

(b)
The graph of equations $x - 2y = 0\ and\ 3x - y = 0$ is as shown in the figure. Since, given point $(a,\ a^{2})$ lies in the shaded region.
[image:10_image2.emf]
$Then,\ a^{2} - \frac{a}{2} > 0$
$and\ a^{2} - 3a < 0$
$\Rightarrow \ a \in ( - \infty,\ 0) \cup \left( \frac{1}{2},\ \infty \right)$
$and\ a \in (0,\ 3)$
$\Rightarrow \ a \in \left( \frac{1}{2},\ 3 \right)$

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

Explanation

Reviewed by Dr. Abubacker

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