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
Perpendicular pair to \(3 x^2-4 x y+5 y^2=0\) is \(5 x^2+4 x y+3 y^2=0\). Equation of lines through \((a, b)\): \(5(x-a)^2+4(x-a)(y-b)+3(y-b)^2=0\). \(5x^2+4xy+3y^2+(-10a-4b)x+(-4a-6b)y+(5a^2+4ab+3b^2)=0\). Comparing with \(l x^2+2 h x y+m y^2-32 x-26 y+c=0\): \(l=5\),…
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