Q104 / 160 · AP EAMCET 2020 (17 Sep Shift 2) · Mathematics

Which of the following pair of straight lines intersect at right angles?

Correct answer
A
\(2 x^2=y(x+2 y)\)
B
\((x+y)^2=x(y+3 x)\)
C
\(2 y(x+y)=x y\)
D
\(y= \pm 2 x\)

Solution

For perpendicular pairs, \(a+b=0\) Now for pairs, \(\begin{aligned} & 2 x^2=y(x+2 y) \\ \Rightarrow \quad & 2 x^2-2 y^2-x y=0 \end{aligned}\) Coefficient of \(x^2+\) coefficient of \(y^2\) \(=2+-2=0\) So, there are perpendicular lines.

Hence, the correct answer is option: 'A'.

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