JEE Advance - Mathematics (1992 - No. 13)
Determine all values of $$\alpha $$ for which the point $$\left( {\alpha ,\,{\alpha ^2}} \right)$$ lies insides the triangle formed by the lines
$$$\matrix{
{2x + 3y - 1 = 0} \cr
{x + 2y - 3 = 0} \cr
{5x - 6y - 1 = 0} \cr
} $$$
$$\alpha \in \left( { - {3 \over 2}, - 1} \right) \cup \left( {{1 \over 2},1} \right)$$
$$\alpha \in \left( { - {5 \over 2}, - 2} \right) \cup \left( {{1 \over 4},{3 \over 4}} \right)$$
$$\alpha \in \left( { - {1 \over 2}, 0} \right) \cup \left( {{3 \over 2},2} \right)$$
$$\alpha \in \left( { - 2, - {3 \over 4}} \right) \cup \left( {1,{5 \over 2}} \right)$$
$$\alpha \in \left( { - {7 \over 2}, - 3} \right) \cup \left( {{1 \over 8},{7 \over 8}} \right)$$
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