JEE Mains · Maths · STD 11 - 9. straight line
If the line \(l_1: 3 y -2 x =3\) is the angular bisector of the lines \(l_2: x - y +1=0\) and \(l_3: \alpha x +\beta y +17=0\), then \(\alpha^2+\beta^2-\alpha-\beta\) is equal to
- A \(348\)
- B \(346\)
- C \(347\)
- D \(345\)
Answer & Solution
Correct Answer
(A) \(348\)
Step-by-step Solution
Detailed explanation
Sol. Point of intersection of \(\ell_1: 3 y -2 x =3\) \(\ell_2: x - y +1=0 \text { is } P \equiv(0,1)\) Which lies on \(\ell_3: \alpha x +\beta y +17=0\), \(\Rightarrow \beta=-17\) Consider a random point \(Q \equiv(-1,0)\) on \(\ell_2: x - y +1=0\), image of \(Q\) about…
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