Question

The lines Mx + y + 1 = 0 & x + ny + 2 = 0 are co-incident then 1/m2 + n2 is equal to:​

Answer 1

Answer:

Above photography has you Answer

ANS IS m - n

Answer 2

Given:

The lines Mx + y + 1 = 0 & x + ny + 2 = 0 are co-incident

To Find:

1/m^2 + n^2 is equal to:​

Solution:

Co-incident lines are those lines that lie exactly on top of each other, by which we can say that the slope and the constant of the lines will also be equal,

First, let us convert the equation into y=mx+c form, we have

$mx+y+1=0\\y=-mx-1$

and,

$x+ny+2=0\\y=\frac{-x}{n} -\frac{2}{n}$

Now first equating the slopes of the lines, which is

$-m=\frac{-1}{n}\\mn=1$

And by equating the constant we have,

$-1=\frac{-2}{n}\\n=2$

So if n=2 then m=1/2

Now putting the value in the required equation we have,

$=\frac{1}{m^2} +n^2\\=4+4\\=8$

Hence, the value of 1/m^2 + n^2 is 8.