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 the conic equation \(2x^2-2xy+3y^2+2x-y-1=0\) using \(1 = \frac{x+2y}{-\lambda}\): \(2x^2-2xy+3y^2+2x\left(\frac{x+2y}{-\lambda}\right)-y\left(\frac{x+2y}{-\lambda}\right)-1\left(\frac{x+2y}{-\lambda}\right)^2=0\) Multiply by \(\lambda^2\) and collect terms:…
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