AP EAMCET · Maths · Pair of Lines
If the angle between the lines joining the origin to the points of intersection of \(x+2 y+\lambda=0\) and \(2 x^2-2 x y+3 y^2+2 x-y-1=0\) is \(\frac{\pi}{2}\), then a value of \(\lambda\) is
- A 1
- B \(\frac{1}{2}\)
- C 2
- D \(\frac{3}{2}\)
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
Homogenize: \(2 x^2-2 x y+3 y^2+(2 x-y)\left(\frac{x+2y}{-\lambda}\right)-1\left(\frac{x+2y}{-\lambda}\right)^2=0\) \(2\lambda^2 x^2 - 2\lambda^2 x y + 3\lambda^2 y^2 - \lambda(2x-y)(x+2y) - (x+2y)^2 = 0\)…
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