First slide

Pair of straight lines

Question

The distance between the two lines represented by the equation $9 x^{2} - 24 xy + 16 y^{2} - 12 x + 16 y - 12 = 0$ is

Moderate

A

$8 / 5$
B

$6 / 5$
C

$11 / 5$
D

None of these

Solution

$9 x^{2} - 24 xy + 16 y^{2} - 12 x + 16 y - 12 = 0$
or $(3 x - 4 y + 2) (3 x - 4 y - 6) = 0$
Hence, the distance between the lines is $\frac{| 6 - (- 2) |}{5} = \frac{8}{5} .$

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