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)

Question

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) (A) 1 (B) 2 (C) 4 (D) 5

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/a8cdcf0ff2c5b5131fa3693025532d4d-.png" /> for the origin to lie inside the triangle slope of the line L 3 must be (0, (5/2)) ∴ Positive integral values of p are 1 and 2 .

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 $L_{3} : p x - y + 6 p - 15 = 0$ is(are)

1

2

4

5

for the origin to lie inside the triangle slope of the line $L_{3}$ must be $(0, \frac{5}{2})$
$∴$ Positive integral values of $p$ are 1 and 2 .

Q. The positive integral value(s) of ' p ' for which the origin lies inside the triangle formed by the lines L1​:15x+2y=30,L2​:5x−y+15=0 and L3​:px−y+6p−15=0 is(are)

1

2

4

5

for the origin to lie inside the triangle slope of the line L3​ must be (0,25​) ∴ Positive integral values of p are 1 and 2 .

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 $L_{3} : p x - y + 6 p - 15 = 0$ is(are)

for the origin to lie inside the triangle slope of the line $L_{3}$ must be $(0, \frac{5}{2})$
$∴$ Positive integral values of $p$ are 1 and 2 .