3x² -11xy -20y² | Pair Of Straight Lines | SciPiPupil

Question: Find the equation of straight lines passing through the origin and perpendicular to the given line: $3x² -11xy -20y² = 0$.

Solution:

Given,

Equation of a single line is $3x² -11xy -20y²= 0$ - (i)

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

$a = 3, 2hxy = -11xy, and b = -20$

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,

$or, -20x² - (-11xy) + 3y² = 0$

$or, -20x² +11xy + 3y² = 0$ 

$or, 20x² -11xy -3y² = 0$ is the required equation.

Therefore, the required single equation of straight lines is 20x² -11xy -3y² = 0.

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