First slide

Equation of line in Straight lines

Question

If the point $P (a^{2}, a)$ lies in the region corresponding to the acute angle between the lines $2 y = x$ and $4 y = x$ , then

Moderate

A

$a \in [2, 4]$
B

$a \in (2, 4]$
C

$a \in [2, 5)$
D

$a \in (2, 4)$

Solution

But $a^{2} > 0$ , hence point $P (a^{2}, a)$ lies in first quadrant. We have
$a - (\frac{a^{2}}{4}) > 0 & a - (\frac{a^{2}}{2}) < 0$
( $∴ (1, 0)$ and P lies on same side of x-2y=0 and (1,0) and P lies opposite sides of x-4y=0)
$\Rightarrow 0 < a a n d a \in (- \infty, 0) \cup (2, \infty)$
$\Rightarrow a \in (2, 4)$

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