Question

Find the two seperate equations when the lines represented by kx^2 + 8xy - 3y^2 = 0 are perpendicular to each other

Answer 1

Answer:

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Answer 2

The joint equation of line given by ax² +2hxy + by² = 0 represents two perpendicular lines iff a + b = 0.

i.e. coefficient of x² + coefficient of y² = 0.

Given equation of line

⟼ kx² +8xy−3y² =0

Since, it represents two perpendicular lines.

It means, coefficient of x² + coefficient of y² = 0.

⟼ k−3=0

⟹ k=3

Now, it can be rewritten as

⟼ 3x² + 8xy − 3y² = 0

⟼ 3x² + 9xy − xy − 3y² = 0

⟼ 3x(x+3y) − y(x+3y)=0

⟼ (x+3y) (3x−y) = 0

⟹ x+3y = 0 and 3x−y = 0