AP EAMCET · Maths · Pair of Lines
If \(\left(\frac{2}{3}, 0\right)\) is the centroid of the triangle formed by the lines \(4 x^2-y^2=0\) and \(l \mathrm{x}+\mathrm{my}+\mathrm{n}=0\), then \(l+\mathrm{m}+\mathrm{n}=\)
- A \(1\)
- B \(0\)
- C \(-1\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(0\)
Step-by-step Solution
Detailed explanation
\(4 x^2-y^2=0 \implies (2x-y)(2x+y)=0 \implies y=2x\) and \(y=-2x\). Vertices: \(A(0,0)\). Intersection of \(y=2x\) and \(lx+my+n=0\): \(lx+m(2x)+n=0 \implies x(l+2m)=-n \implies B\left(-\frac{n}{l+2m}, -\frac{2n}{l+2m}\right)\). Intersection of \(y=-2x\) and \(lx+my+n=0\):…
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