AP EAMCET · Maths · Straight Lines
The lines \((a+2 b) x+(a-3 b) y=a-b\) for different values of \(a\) and \(b\) pass through the fixed point whose coordinates are
- A \(\left(\frac{2}{5}, \frac{2}{5}\right)\)
- B \(\left(\frac{3}{5}, \frac{3}{5}\right)\)
- C \(\left(\frac{2}{5}, \frac{3}{5}\right)\)
- D \(\left(\frac{3}{5}, \frac{2}{5}\right)\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{2}{5}, \frac{3}{5}\right)\)
Step-by-step Solution
Detailed explanation
Given, equation of line is \[ \begin{array}{rlrl} & & (a+2 b) x+(a-3 b) y & =a-b \\ \Rightarrow & a x+2 b x+a y-3 b y & =a-b \\ \Rightarrow & a(x+y-1)+b(2 x-3 y+1) & =0 \end{array} \] Equating the coefficient, we obtain \[ \begin{array}{r} x+y-1=0 \\ 2 x-3 y+1=0 \end{array} \]…
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