AP EAMCET · Maths · Pair of Lines
One line of the pair of lines \(x^2+x y-2 y^2=0\) is perpendicular to one line of the pair of lines \(3 y^2-5 x y-2 x^2=0\). If the combined equation of the two lines other than those two perpendicular lines is \(a x^2+2 h x y+b y^2=0\), then \(a+2 h+b=\)
- A -1
- B 1
- C 0
- D -5
Answer & Solution
Correct Answer
(C) 0
Step-by-step Solution
Detailed explanation
\(x^2+xy-2y^2=0 \implies (x+2y)(x-y)=0\) \(3y^2-5xy-2x^2=0 \implies (2x-y)(x+3y)=0\) Lines \(x+2y=0\) (slope \(-1/2\)) and \(2x-y=0\) (slope \(2\)) are perpendicular. The other lines are \(x-y=0\) and \(x+3y=0\). Combined equation: \((x-y)(x+3y)=0 \implies x^2+2xy-3y^2=0\)…
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