x²+3xy+2y²=0 | Pair Of Straight Lines | SciPiPupil

Question: Find the equation of straight lines passing through the origin and perpendicular to the given line: $x² +3xy +2y² = 0$.

Solution:

Given,

Equation of a single line is $x² +3xy +2y²= 0$ - (i)

Comparing equation (i) with ax²+ 2hxy +by²=0, we get,

$a = 1, 2hxy = 3xy, and b = 2$

We know,

The equation of any line passing through the origin and perpendicular to the line represented by ax² +2hxy +by² = 0 is bx² -2hxy +ay²= 0.

Put value of a, 2hxy and b in bx² -2hxy +ay² = 0, we get,

$or, 2x² - 3xy + 1y² = 0$

$or, 2x² -3xy + y² = 0$ is the required equation.

Therefore, the required single equation of straight lines is 2x² -3xy +y² = 0.

#SciPiPupil