MHT CET · Maths · Pair of Lines
The joint equation of two lines passing through the origin and perpendicular to the lines given by \(2 x^2+5 x y+3 y^2=0\) is
- A \(3 x^2+5 x y+2 y^2=0\)
- B \(3 x^2-5 x y+2 y^2=0\)
- C \(3 x^2-5 x y-2 y^2=0\)
- D \(2 x^2-5 x y+3 y^2=0\)
Answer & Solution
Correct Answer
(B) \(3 x^2-5 x y+2 y^2=0\)
Step-by-step Solution
Detailed explanation
\(2 x^2+5 x y+3 y^2=0 \Rightarrow(x+y)(2 x+3 y)=0\)
lines are \(x+y=0\) and \(2 x+3 y=0\)
so, perpendicular lines are \(x-y=0\) and \(3 x-2 y=0\)
joint equation \((x-y)(3 x-2 y)=0\)
\(\Rightarrow 3 x^2-5 x y+2 y^2=0\)
lines are \(x+y=0\) and \(2 x+3 y=0\)
so, perpendicular lines are \(x-y=0\) and \(3 x-2 y=0\)
joint equation \((x-y)(3 x-2 y)=0\)
\(\Rightarrow 3 x^2-5 x y+2 y^2=0\)
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