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  4. The positive integral value(s) of ' p ' for which the origin lies inside the triangle formed by the lines L 1: 15 x +2 y =30, L 2: 5 x - y +15=0 and L 3: px - y +6 p -15=0 is(are)

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Q. The positive integral value(s) of ' $p$ ' for which the origin lies inside the triangle formed by the lines $L _1: 15 x +2 y =30, L _2: 5 x - y +15=0$ and $L _3: px - y +6 p -15=0$ is(are)

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Solution:

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for the origin to lie inside the triangle slope of the line $L _3$ must be $\left(0, \frac{5}{2}\right)$
$\therefore$ Positive integral values of $p$ are 1 and 2 .