JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(\mathrm{A}(-1,1)\) and \(\mathrm{B}(2,3)\) be two points and \(\mathrm{P}\) be a variable point above the line \(A B\) such that the area of \(\triangle \mathrm{PAB}\) is \(10\) . If the locus of \(\mathrm{P}\) is \(\mathrm{ax}+\mathrm{by}=15\), then \(5 a+2 b\) is :
- A \(-\frac{12}{5}\)
- B \(-\frac{6}{5}\)
- C \(4\)
- D \(6\)
Answer & Solution
Correct Answer
(A) \(-\frac{12}{5}\)
Step-by-step Solution
Detailed explanation
\(\frac{1}{2}\left|\begin{array}{lll}\mathrm{h} & \mathrm{k} & 1 \\ -1 & 1 & 1 \\ 2 & 3 & 1\end{array}\right|=10\) \( -2 x+3 y=25 \) \( -\frac{6}{5} x+\frac{9}{5} y=15 \) \( a=-\frac{6}{5}, b=\frac{9}{5} \) \( 5 a=-6,2 b=\frac{18}{5}\)
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