AP EAMCET · Maths · Pair of Lines
If the pair of lines represented by \(3 x^2-5 x y+P y^2=0\) and \(6 x^2-x y-5 y^2=0\) have one line in common, then the sum of all possible values of \(P\) is
- A \(\frac{33}{4}\)
- B \(\frac{17}{4}\)
- C \(-\frac{33}{4}\)
- D \(-\frac{17}{4}\)
Answer & Solution
Correct Answer
(D) \(-\frac{17}{4}\)
Step-by-step Solution
Detailed explanation
\(6 x^2-x y-5 y^2=0\) \(\Rightarrow(6 x+5 y)(x-y)=0 \Rightarrow y=x\) or \(y=\frac{-6 x}{5}\) When \(y=x, 3 x^2-5 x^2+P x^2=0 \Rightarrow P=2\) When \(y=-\frac{6 x}{5} ; 3 x^2-5 x\left(\frac{-6 x}{5}\right)+\frac{36 x^2}{25} P=0\)…
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