Question

Equation of the line having intercepts a,b on the axes such that a+b=5 ,ab=6 is

Answer 1

$\textsf{Given:}$

$\mathsf{a+b=5\\\\ab=6}$

$\implies\mathsf{b=5-a\;\&\;ab=6}$

$\implies\mathsf{a(5-a)=6}$

$\implies\mathsf{5a-a^2=6}$

$\implies\mathsf{-a^2+5a-6=0}$

$\implies\mathsf{a^2-5a+6=0}$

$\implies\mathsf{(a-2)(a-3)=0}$

$\implies\mathsf{a=2,3}$

$\textsf{when\,a=3, b=2}$

$\textsf{The line is }\mathsf{\frac{x}{a}+\frac{y}{b}=1}$

$\implies\mathsf{\frac{x}{3}+\frac{y}{2}=1}$

$\implies\mathsf{\bf\,2x+3y-6=0}$

$\textsf{when\,a=2, b=3}$

$\implies\mathsf{\frac{x}{2}+\frac{y}{2}=1}$

$\implies\mathsf{\bf\,3x+2y-6=0}$

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Find the equation of line passing through the point (5,6) and making equal intercept on x & y axis​

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Answer 2

Step-by-step explanation:

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