The lines represented by the equation x2+2√3xy+3y2-3x-3√3y-4=0 , are

Question

The lines represented by the equation x2+2√3xy+3y2-3x-3√3y-4=0 , are (A) perpendicular to each other (B) parallel (C) inclined at 45o to each other (D) None of these

Tardigrade Admin · Accepted Answer

The given equation can be written as (. x + √3 y .)2 - 3 (. x + √3 y .) - 4 = 0 ⇒ x + √3 y + 1 = 0 , x + √3 y = 4 Hence, given equation represents two parallel lines

Q. The lines represented by the equation $x^{2} + 23 x y + 3 y^{2} - 3 x - 33 y - 4 = 0$ , are

perpendicular to each other

parallel

inclined at $4 5^{o}$ to each other

None of these

The given equation can be written as $(x + 3 y)^{2} - 3 (x + 3 y) - 4 = 0$
$\Rightarrow x + 3 y + 1 = 0, x + 3 y = 4$
Hence, given equation represents two parallel lines

Q. The lines represented by the equation x2+23​xy+3y2−3x−33​y−4=0 , are