AP EAMCET · Maths · Pair of Lines
The combined equation of the lines passing through the origin and having slopes \(\frac{2}{3}\) and \(\frac{-2}{3}\) is
- A \(2 x^2-9 y^2=0\)
- B \(4 x^2-x y-9 y^2=0\)
- C \(4 x^2-9 y^2=0\)
- D \(4 x^2+x y-9 y^2=0\)
Answer & Solution
Correct Answer
(C) \(4 x^2-9 y^2=0\)
Step-by-step Solution
Detailed explanation
The equation of lines passes through origin having slopes \(\frac{2}{3}\) and \(-\frac{2}{3}\) are respectively \(2 x+3 y=0\) and \(2 x-3 y=0\), so combined equation is \(\begin{array}{rlrl} & & (2 x-3 y)(2 x+3 y) & =0 \\ \Rightarrow & 4 x^2-9 y^2 & =0. \end{array}\)
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