Question

The distance between the lines represented by the equation 4x² + 4xy + y² − 6x − 3y − 4 = 0 is

Options

• \[\frac{1}{\sqrt{5}}\] units

• \[\frac{1}{5}\] units

• √5 units

• 5 units

Answer 1

√5 units

Explanation:

4x² + 4xy + y² − 6x − 3y − 4 = 0

∴ (2x + y)² − 3(2x + y) − 4 = 0

∴ (2x + y − 4)(2x + y + 1) = 0

∴ The separate equations of lines are
2x + y − 4 = 0
and 2x + y + 1 = 0

∴ Distance between the lines = \[\frac{1+4}{\sqrt{4+1}}\]
\[=\frac{5}{\sqrt{5}}=\sqrt{5}\mathrm{units}\]