Question

the angle between the straight lines represented by the equation y ^2 - xy - 6x^2 =0 is​

Answer 1

Answer:

hi

Step-by-step explanation:

the answer is in the attachment.

Answer 2

$\sf{Let \: 2 \: line \: represented \: by \: {ax}^{2} +2hxy+ {by}^{2} = 0:-}$

$\sf{y = m1x}$

$\sf{y=m2x}$

Where,

$\sf{m1+m2 = \frac{ - 2h}{b} }---(1)$

$\sf{And, m1m2 = \frac{a}{b} }---(2)$

$\sf{Let \: θ \: be \: angle \: between \: two \: lines}$

$\sf{tanθ= \frac{ + 2\sqrt{ {h}^{2} -ab } }{a + b}} - - - (3)$

Calculation:-

$\sf{Given \: equation \: is:-}$

$\sf{ {y}^{2} - xy - {6x}^{2} = 0}$

$\sf{Compare \: it \: with \: standard \: equation}$

$\sf{ {ax}^{2} + 2hxy + {by}^{2} } = 0$

$\sf{b = 1.a = - 6.h = \frac{ - 1}{2}}$

From equ.1)

$\sf{tan \: θ= \frac{ + 2 \sqrt{ (\frac{ { - 1} }{2} )^{2 } - ( - 6)(1)} }{ - 6 + 1} }$

$\sf{tanθ= \frac{ + 2 \sqrt{ \frac{1}{4} + 6} }{ - 5} }$

$\sf{tanθ= \frac{ + 2 \times \frac{5}{2} }{ - 5} = ±1}$

$\sf{θ=45°}$