TS EAMCET · Maths · Pair of Lines
If \(\alpha\) represent the square of the distance between the origin and the point of intersection of the lines \(x^2-y^2-x+3 y-2=0\) and \(\beta\) represent the product of the perpendicular distances from the origin on the pair of lines, then \(\alpha \beta=\)
- A \(\frac{5}{4}\)
- B 1
- C \(\left(\frac{5}{2}\right)^{0.5}\)
- D 2
Answer & Solution
Correct Answer
(C) \(\left(\frac{5}{2}\right)^{0.5}\)
Step-by-step Solution
Detailed explanation
We have, pair of straight line is \(\begin{gathered} x^2-y^2-x+3 y-2=0 \\ (x-y+1)(x+y-2)=0 \\ x-y+1=0 \text { and } x+y-2=0 \end{gathered}\) Solving these equation, we get \(x=\frac{1}{2} \text { and } y=\frac{3}{2}\) \(\therefore\) Intersection point…
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