AP EAMCET · Maths · Pair of Lines
The figure formed by the pairs of lines \(6 x^2+13 x y+6 y^2=0\) and \(6 x^2+13 x y+6 y^2+10 x+10 y+4=0\), is a
- A Square
- B Parallelogram
- C Rhombus
- D Rectangle
Answer & Solution
Correct Answer
(C) Rhombus
Step-by-step Solution
Detailed explanation
(c) Equation of pair of lines, \[ \begin{aligned} & 6 x^2+13 x y+6 y^2=0 \\ & 6 x^2+9 x y+4 x y+6 y^2=0 \\ & 3 x(2 x+3 y)+2 y(2 x+3 y)=0 \\ & (3 x+2 y)(2 x+3 y)=0 \\ & \therefore \quad 3 x+2 y=0 \text { and } 2 x+3 y=0 \end{aligned} \] Similarly, for another equation of pairs of…
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