First slide

Equation of line in Straight lines

Question

If the point $P (α^{2}, α)$ lies in the region corresponding to the acute angle between the lines $x - 3 y = 0$ and $x - 5 y = 0$ then

Moderate

A

$α \in (5, 15)$
B

$α \in (5, 8)$
C

$α \in (4, 8)$
D

$α \in (3, 5)$

Solution

P lies in the acute angle
$\Rightarrow α^{2} - 3 α > 0$ and $α^{2} - 5 α < 0$
$\Rightarrow α \in (- \infty, 0) \cup (3, \infty)$ and $α \in (0, 5)$
$∴ α \in (3, 5)$

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