AP EAMCET · Maths · Pair of Lines
If the equation of the pair of straight lines intersecting at \((a, b)\) and perpendicular to the pair of lines \(3 x^2-4 x y+5 y^2=0\) is \(l x^2+2 h x y+m y^2-32 x-26 y+c=0\), then \(\frac{a+b+c}{l+h+m}=\)
- A \(\frac{38}{5}\)
- B \(\frac{17}{2}\)
- C \(\frac{15}{6}\)
- D \(\frac{49}{6}\)
Answer & Solution
Correct Answer
(A) \(\frac{38}{5}\)
Step-by-step Solution
Detailed explanation
Given lines: \(3 x^2-4 x y+5 y^2=0 \Rightarrow A=3, 2H=-4, B=5\). Equation of perpendicular lines through \((a,b)\) is \(B(x-a)^2 - 2H(x-a)(y-b) + A(y-b)^2 = 0\). \(5(x-a)^2 + 4(x-a)(y-b) + 3(y-b)^2 = 0\) \(5x^2 + 4xy + 3y^2 + (-10a-4b)x + (-4a-6b)y + (5a^2+4ab+3b^2) = 0\)…
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