Question

23) If the angle between the two lines represented by
2x² + 5xy + 3y2 +6x + 7y+4=0 is tan'm, then
m =

a)1/5 b) 1 c)7/5 d) 7​

Answer 1

Option : A

Option : A Answer : m = 1/5

The angle between the lines represented by the lines ax² + 2hxy + by² + 2gx + 2fy + c = 0 is given by,

$\tan( \theta) = \frac{ \pm2 \sqrt{ {h}^{2} - ab} }{a + b}$

Given equation of pair of lines is,

2x² + 5xy + 3y²+6x + 7y+4=0

So,

a = 2

b = 3

2h = 5

Angle between the lines is,

$\tan( \theta) = \frac{ \pm2 \sqrt{ {h}^{2} - ab} }{a + b} \\ \\ \tan( \theta) = \frac{ 2 \sqrt{ ({ \frac{5}{2} )}^{2} - (2)(3) } }{2 + 3} \\ \\ tan \theta = \: \frac{2\sqrt{ \frac{25}{4} - 6} }{5} \\ \\ tan \theta = \frac{ 2\sqrt{ \frac{25 - 24 }{4} } }{5} \\ \\ \tan \theta \: = \frac{2 \sqrt{ \frac{1}{4} } }{5} \\ \\ \tan \theta = \frac{2 \frac{1}{2} }{5} \\ \\ \tan \theta \: = \frac{1}{5} \\ \\ \theta \: = {tan}^{ - 1} ( \frac{1}{5} )</p><p>$

Given,

$\theta \: = {tan}^{ - 1} m = {tan}^{ - 1} ( \frac{1}{5} )$

Therefore, m = 1/5.