Question

10. Find the equations of the lines whose sum and product of intercepts are 1 and ‐6 respectively​

Answer 1

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Let the intercepts cut by the given line on the axes be a and b.

It is given that,  

a+b= 1....(1)

and ab=−6....(2)

On solving equation (1) and (2), we obtain

a=3 and b=−2 or a=−2 and b=3

It is known that the equation of the line whose intercepts on the axes are a and b is $\bold{\frac{x}{a}+\frac{y}{b}=1 }$   or bx+ay−ab=0.

case1: a=3 and b=−2  

In this case, the equation of the line is −2x+3y+6=0⇒2x−3y=6

case2: a=−2 and b=3

In this case, the equation of a line is 3x−2y+6=0⇒−3x+2y=6

Thus, the required equation of the lines are 2x−3y=6 and −3x+2y=6.

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Answer 2

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AnsweR:

Let the intercepts cut by the given line on the axes be a and b.

It is given that,

a+b= 1....(1)

and ab=−6....(2)

On solving equation (1) and (2), we obtain

a=3 and b=−2 or a=−2 and b=3

It is known that the equation of the line whose intercepts on the axes are a and b is

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

aa + by

=1 or bx+ay−ab=0.

case1: a=3 and b=−2

In this case, the equation of the line is −2x+3y+6=0⇒2x−3y=6

case2: a=−2 and b=3

In this case, the equation of a line is 3x−2y+6=0⇒−3x+2y=6

Thus, the required equation of the lines are 2x−3y=6 and −3x+2y=6.

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