Question

If the points (–2, 1) and (–1, – 2) are on the opposite sides of the line 2x + y + a = 0, then the set of values of a is _________.

Answer 1

For given line 2x + y + a = 0
(−2, 1) and (−1, −2) lie on opposite sides
i.e. 2(−2) + 1 + a = −4 + 1 + a = −3 + a and 2(−1) + (−2) + a = −2 − 2 + a

= −4 + a

i.e. −3 + a > 0 and −4 + a < 0
i.e. a > 3 and a < 4
i.e. a lies in (3, 4)