AP EAMCET · Maths · Pair of Lines
If the combined equation of the lines joining the origin to the points of intersection of the curve \(x^2+y^2-2 x-4 y+2=0\) and the line \(x+y-2=0\) is \(\left(l_1 x+m_1 y\right)\) \(\left(l_2 \mathrm{x}+\mathrm{m}_2 \mathrm{y}\right)=0\), then \(l_1+l_2+\mathrm{m}_1+\mathrm{m}_2=\)
- A \(16\)
- B \(-6\)
- C \(-2\)
- D \(10\)
Answer & Solution
Correct Answer
(C) \(-2\)
Step-by-step Solution
Detailed explanation
\(1 = \frac{x+y}{2}\) \(x^2+y^2-2 x\left(\frac{x+y}{2}\right)-4 y\left(\frac{x+y}{2}\right)+2\left(\frac{x+y}{2}\right)^2=0\) \(x^2+y^2-(x^2+xy)-(2xy+2y^2)+\frac{x^2+2xy+y^2}{2}=0\) \(-xy-y^2-2xy+\frac{x^2+2xy+y^2}{2}=0\) \(-3xy-y^2+\frac{x^2+2xy+y^2}{2}=0\)…
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