Question

find the equation of the straight lines which passes through the point 3,2 and cut off intercepts A and B respectively on x and y axis such that a-b=2

Answer 1

Answer:

$\textsf{The required lines are 2x+3y-12= and x-y-1=0}$

Step-by-step explanation:

$\text{The equation of the line in intercept form is}$

$\bf\frac{x}{a}+\frac{y}{b}=1$

$\text{Since it passes through (3,2), we have}$

$\frac{3}{a}+\frac{2}{b}=1$

$\text{But }a=b+2$

$\implies\frac{3}{b+2}+\frac{2}{b}=1$

$\implies\frac{3b+2(b+2)}{b(b+2)}=1$

$\implies\,3b+2b+4=b^2+2b$

$\implies\,b^2-3b-4=0$

$\implies\,(b-4)(b+1)=0$

$\implies\,b=4,\;-1$

$\text{when b=4, }a=6$

$\text{The line is }\frac{x}{6}+\frac{y}{4}=1$

$4x+6y=24$

$\implies\bf\,2x+3y-12=0$

$\text{when b=-1, }a=1$

$\text{The line is }\frac{x}{1}+\frac{y}{-1}=1$

$-x+y=-1$

$\implies\bf\,x-y-1=0$

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