Question

the equation of the line passing through (-2,1) and having intercepts whose product is 1 is​

Answer 1

GIVEN :

The equation of the line passing through (-2,1) and having intercepts whose product is 1 ​

TO FIND :

The equation of the line passing through (-2,1) and having intercepts whose product is 1

SOLUTION :

Given that the equation of the line passing through (-2,1) and having intercepts whose product is 1

The formula for equation of the line in the intercept form is

$\frac{x}{a}+\frac{y}{b}=1\hfill (1)$

where a and b are intercepts on x and y axes respectively.  

It is given that ab=1

⇒ $a=\frac{1}{b}\hfill (2)$

From equation (1), we obtain

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

$bx+\frac{y}{b}=1$

Since it is passing through (-2,1)

Substitute x=-2 and y=1

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

​$-2b+\frac{1}{b}=1$

​$\frac{-2b^2+1}{b}=1$

$-2b^2+1=b$

$-2b^2+1-b=0$

$-(2b^2-1+b)=0$

$2b^2-1+b=0$

$2b^2+b-1=0$

$2b^2-b+2b-1=0$

b(2b-1)+1(2b-1)=0

(b+1)(2b-1)=0  

b+1=0 or 2b-1=0

⇒ b=-1 and $b=\frac{1}{2}$

If b=-1 ⇒ $a=\frac{1}{-1}$

⇒ a=-1, then the equation of the line is

$\frac{x}{-1}+\frac{y}{-1}=1$

-x-y=1

-x-y-1=0

x+y+1=0

And if $b=\frac{1}{2}$ ⇒ $a=\frac{1}{\frac{1}{2}}$

a=2 , then the equation of the line is

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

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

$\frac{x+4y}{2}=1$

x+4y=2

x+4y-2=0

Answer 2

Answer:

x+y+1=0 or x+4y-2=0

Step-by-step explanation:

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