First slide

Equation of line in Straight lines

Question

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

Moderate

A

$(0, \frac{1}{2})$
B

$(3, \infty)$
C

$(\frac{1}{2}, 3)$
D

$(- 3, - \frac{1}{2})$

Solution

Clearly , point $(a, a^{2})$ lies on the opposite sides of
the two lines .
$\begin{array}{l} ∴ (\frac{a}{2} - a^{2}) (3 a - a^{2}) < 0 \\ \Rightarrow a^{2} (1 - 2 a) (3 - a) < 0 \\ \Rightarrow (2 a - 1) (a - 3) < 0 \Rightarrow \frac{1}{2} < a < 3 \Rightarrow a \in (1 / 2, 3) \end{array}$

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