TS EAMCET · Maths · Pair of Lines
Suppose \(O(0,0)\) is the origin and the line \(L=x+y-\lambda=0\) meets the curve \(x^2+y^2-2 x-4 y+2=0\) at \(A\) and \(B\). If \(\angle A O B=90^{\circ}\), then the distance between such lines \(L=0\) is
- A \(\frac{1}{\sqrt{2}}\)
- B \(\frac{3}{\sqrt{2}}\)
- C \(\sqrt{2}\)
- D \(\sqrt{2}+1\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{\sqrt{2}}\)
Step-by-step Solution
Detailed explanation
The combined equation of pair of lines joining point of intersection \(A\) and \(B\) of the line \(L=x+y-\lambda=0\) and the curve \(x^2+y^2-2 x-4 y+2=0\) to the origin ' \(O\) ' is \(x^2+y^2-2(x+2 y)\left(\frac{x+y}{\lambda}\right)+2\left(\frac{x+y}{\lambda}\right)^2=0\) Since,…
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