TS EAMCET · Maths · Pair of Lines
If the pair of lines joining the origin to the points of intersection of the line \(x+y=1\) with the curve \(x^2+y^2+2 h x y+g x+f y+1=0\) are at right angles, then the point \((g, f)\) lies on the line
- A \(2 x+y=5\)
- B \(x-y=4\)
- C \(x+y+4=0\)
- D \(x+2 y=5\)
Answer & Solution
Correct Answer
(C) \(x+y+4=0\)
Step-by-step Solution
Detailed explanation
Equation of line is \(x+y=1\) ...(i) and equation of the curve is \(x^2+y^2+2 h x y-g x-f y+1=0\) ...(ii) Making Eq. (ii) homogeneous by Eq. (i), we get the equation of the lines joining the origin to the point of intersection of Eqs. (i) and (ii).…
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