Question

Distance between the pair of lines represented by the equation $x^{2} - 6xy + 9y^{2} + 3x - 9y - 4 = 0$

• A. $\frac{15}{\sqrt{10}}$
• B. $\frac{1}{2}$
• C. $\sqrt{\frac{5}{2}}$
• D. $\frac{1}{\sqrt{10}}$

Answer 1

Answer: (C)

$\sqrt{\frac{5}{2}}$

Answer 2

The distance between the pair of straight lines given by

$ax^{2} + 2hxy + by^{2} + 2gx + 2fy + c = 0$ is $2\sqrt{\frac{g^{2} - ac}{a(a + b)}}$,

Here $a = 1,b = 9,c = 4,g = \frac{3}{2} = 2 \times \sqrt{\frac{\frac{9}{4} - ( - 4)}{1(1 + 9)}} = 2 \times \sqrt{\frac{\frac{25}{4}}{10}} = \sqrt{\frac{5}{2}}$