TS EAMCET · Maths · Pair of Lines
For \(a, b, c \in \mathbb{R}\), if \(6 a^2-3 b^2-c^2+7 a b-a c+4 b c=0\) and \(|a|+|b| \neq 0\), then all the lines given by \(a x+b y+c=0\) are
- A concurrent at \((3,1)\) or \((1,3)\)
- B parallel to each other \(\forall a, b, c \in \mathbb{R}\)
- C concurrent at \((-2,-3)\) or \((3,-1)\)
- D concurrent at \((2,3)\) or \((-3,1)\)
Answer & Solution
Correct Answer
(C) concurrent at \((-2,-3)\) or \((3,-1)\)
Step-by-step Solution
Detailed explanation
We have \(6 a^2-3 b^2-c^2+7 a b-a c+4 b c=0\) where a, b, c, \(\in \mathbf{R}\) \( \Rightarrow 6 {a}^2+{a}(7 {~b}-{c})-3 {~b}^2-{c}^2+4 {bc}=0 \) On solving we get \( \Rightarrow a=\frac{(c-7 b) \pm(11 b-5 c)}{12} \) Solving equations (i) and (ii) with \({ax}+{by}+{c}=0\) one by…
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