TS EAMCET · Maths · Pair of Lines
If \(x^2+\alpha y^2+2 \beta y=a^2\) represents a pair of perpendicular lines, then \(\beta\) equals to
- A \(4 a\)
- B \(a\)
- C \(2a\)
- D \(3a\)
Answer & Solution
Correct Answer
(B) \(a\)
Step-by-step Solution
Detailed explanation
Let given line be \[ x^2+\alpha y^2+2 \beta y-a^2=0 \] Here, \(a=1, b=\alpha, h=0, g=0, f=\beta, c=-a^2\) Condition for perpendicular line \(a+b=0\) \[ \therefore \quad 1+\alpha=0 \Rightarrow \alpha=-1 \] Condition of pair of lines…
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