AP EAMCET · Maths · Pair of Lines
The pair of lines joining the origin to the points of intersection of the line \(x-y=2\) with the curve \(5 x^2+12 x y-8 y^2+8 x-4 y+12=0\) are equally inclined to the pair of lines
- A \(x^2-x y=0\)
- B \(x y=0\)
- C \((x-2)(y-2)=0\)
- D \(x y-y^2=4\)
Answer & Solution
Correct Answer
(B) \(x y=0\)
Step-by-step Solution
Detailed explanation
\(5 x^2+12 x y-8 y^2+8 x\left(\frac{x-y}{2}\right)-4 y\left(\frac{x-y}{2}\right)+12\left(\frac{x-y}{2}\right)^2=0\) \(5 x^2+12 x y-8 y^2+4 x(x-y)-2 y(x-y)+3(x-y)^2=0\) \(5 x^2+12 x y-8 y^2+4 x^2-4 x y-2 x y+2 y^2+3 x^2-6 x y+3 y^2=0\) \(12 x^2 - 3 y^2 = 0\) \(4 x^2 - y^2 = 0\)…
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