Question

Question No. 94 :

Show that the equation
${x}^{2}+3xy+2{y}^{2}=0$
represents a pair of straight lines. Find these straight lines and the angle between them.

Answer 1

x² + 3xy + 2y² = 0.

x² + xy + 2xy + 2y² = 0

x(x + y) + 2y(x + y) = 0

(x + y)(x + 2y) = 0


So, these two lines are

x + y = 0

x + 2y = 0

Slope of first line is -1.

As on comparing it with y = mx + c

y = -x

So, m1 = -1.


Similarly, Slope of second line is -1/2.

m2 = -1/2.

Let the angle be @.

Use the formula

tan@ = ± (m1 - m2) / (1 + m1m2)

Putting values of m1 and m2,

tan@ = ± [ -1 - (-1/2) ] / [ 1 + (-1)(-1/2) ]

tan@ = ± ( -1 / 2 ) / ( 3 / 2 )

tan@ = ± (-1/3)

tan@ = ± 1/3

@ = tan inverse ± 1/3

One angle would be obtuse and another would be acute.

Thank you.

Answer 2

PLZ refer to the attachment for answer

hope it helps

BE BRAINLY//