TS EAMCET · Maths · Pair of Lines
The line \(x+y=k\) meets the pair of straight lines \(x^2+y^2-2 x-4 y+2=0\) at two points \(A\) and \(B\). If \(O\) is the origin and \(\angle A O B=90^{\circ}\), then the value of \(k(>1)\) is
- A 5
- B 4
- C 3
- D 2
Answer & Solution
Correct Answer
(D) 2
Step-by-step Solution
Detailed explanation
Homogenise the pair of lines \(x^2+y^2-2 x-4 y+2=0\) through \(x+y=k\), we get \[ \begin{aligned} & x^2+y^2-2 x\left(\frac{x+y}{k}\right)-4 y\left(\frac{x+y}{k}\right) \\ &+2\left(\frac{x+y}{k}\right)^2=0 \end{aligned} \] Since, intersection points of line and pair of lines make…
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