JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let the system of equations :
\(\begin{aligned}
& 2 x+3 y+5 z=9 \\
& 7 x+3 y-2 z=8 \\
& 12 x+3 y-(4+\lambda) z=16-\mu
\end{aligned}\)
have infinitely many solutions. Then the radius of the circle centred at \((\lambda, \mu)\) and touching the line \(4 x=3 y\) is
- A \(\frac{17}{5}\)
- B \(\frac{7}{5}\)
- C 7
- D \(\frac{21}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{7}{5}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \left|\begin{array}{ccc}2 & 3 & 5 \\ 7 & 3 & -2 \\ 12 & 3 & -(\lambda+4)\end{array}\right|=0 \\ & \Rightarrow 12(-21)-3(-39)-(\lambda+4)(-15)=0 \\ & \Rightarrow-252+117+15(1+4)=0 \\ & \Rightarrow 15 \lambda+177-252=0 \\ & \Rightarrow 15 \lambda-75=0 \Rightarrow…
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