AP EAMCET · Maths · Pair of Lines
The equation of the pair of lines joining the origin to the points of intersection of \(x^2+y^2=9\) and \(x+y=3\), is
- A \(x^2+(3-y)^2=9\)
- B \((3+y)^2+y^2=9\)
- C \(x^2 - y^2 = 9\)
- D \(xy = 0\)
Answer & Solution
Correct Answer
(D) \(xy = 0\)
Step-by-step Solution
Detailed explanation
Given, \(x^2+y^2=9\) and \(x+y=3\) Equation of pair of lines. \(\begin{aligned} & x^2+y^2=9\left(\frac{x+y}{3}\right)^2 \\ & \Rightarrow \quad x^2+y^2=(x+y)^2 \end{aligned}\) \(\begin{aligned} & \Rightarrow \quad x^2+y^2=x^2+y^2+2 x y \\ & \therefore \quad x y=0\end{aligned}\)
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