Question

Consider the family of lines $5x+3y-2+{\lambda }_1(3x-y-4)=0$ and $x-y+1+{\lambda }_2(2x-y-2)=0$.Equation of a straight line that belong to families is -

• A. 25 x - 62 y + 86 = 0
• B. 62x - 25y + 86 = 0
• C. 25 x - 62 y = 86
• D. 5x - 2y - 7 = 0

Answer 1

Answer: (D)

5x - 2y - 7 = 0

$5x+3y-2=0$
$(3x-y-4=0)\times 3$
$14x-10=0$
$x=\frac{5}{7}$
$5\times \frac{5}{7}+3y-2=0$
$3y+\frac{-14+15}{7}=0$
$3y=\frac{-1}{7}\Rightarrow y=-1/21$
$P(\frac{5}{7},\frac{-1}{21})$
Similarity $x-y+1=0$
$\underset{–}{\underset{-}{2}x-\underset{+}{y}-\underset{+}{2}=0}$
$-x+1=0,x=1$ and $y=2$
$Q(I,2)$
equation of line passing through P & Q
$5x+3y02=0$
$\underset{–}{3x-y-4=0)\times 3}$
$14x-14=0$
$x=1$
$y=-1$
$P(I,-)$
$2X-Y-2=0$
$\underset{–}{\underset{-}{x}-\underset{+}{y}\underset{-}{1}=0}$
$x-3=0$
$x=3$
$y=4$
$Q(3,4)$
Equation of line PQ
$y+1=\frac{4+1}{3-1}(x-1)$
$y+1=\frac{5}{2}(x-1)$
$2y+2=5x-5$
$5x-2y-7=0$