Question

If P(α, β) be a point on the line 3x + y = 0 such that the point P and the point Q(1, 1) lie on either side of the line 3x = 4y + 8, then _______.

Options

• `alpha > 8/15, beta < (- 8)/5`

• `alpha < 8/15, beta < (- 8)/5`

• `alpha > 8/15, beta > (- 8)/5`

• `alpha < 8/15, beta > (- 8)/5`

Answer 1

If P(α, β) be a point on the line 3x + y = 0 such that the point P and the point Q(1, 1) lie on either side of the line 3x = 4y + 8, then `underline(alpha > 8/15, beta < (- 8)/5)`.

Explanation:

Point Q (1, 1) lie on either side of L ≡ 3x - 4y - 8 = 0.

∴ `"L"_(1, 1) = 3(1) - 4(1) - 8 > 0   ...["y" = - 3x]`

`=> x > 8/15    => alpha > 8/15`

3x - 4y - 8 > 0

⇒ - y - 4y - 8 > 0    .....[3x = - y]

⇒ y < `- 8/5`

⇒ β < `- 8/5`