Question

4x+py+8=0 and 4x+4y+2=0
are parallel to each other then find the value of p​

Answer 1

$\textbf{Concept used:}$

$\textbf{If the lines are parallel, their slopes are equal}$

$\text{Given lines are}$

$\textbf{4x+py+8=0 and 4x+4y+2=0}$

$\text{Slope of 4x+py+8=0 is \bf\,m_1=\displaystyle\frac{-4}{p} }$

$\text{Slope of 4x+4y+2=0 is \bf\,m_2=\displaystyle\frac{-4}{4}=-1 }$

$\text{Since the lines are parallel, we have}\bf\;m_1=m_2$

$\implies\displaystyle\frac{-4}{p}=-1$

$\implies\boxed{\bf\,p=4}$

$\therefore\textbf{The value of p is 4}$

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Answer 2

Given:

$4x+py+8=0$...(equation 1)

$4x+4y+2=0$...(equation 2)

To Find:

Value of p = ?

Solution:

As we know that if the lines are parallel to each other then their slopes are equal.

So that,

Slope of equation 1 i.e., 4x+py+8=0

$m1=\frac{-4}{p}$

Slope of equation 2 i.e., 4x+4y+2=0

$m2=\frac{-4}{4}=-1$

Now,

If the lines are parallel, then

⇒  $m1=m2$

⇒  $\frac{-4}{p}=-1$

⇒  $-4=-p$

⇒  $p=4$

Thus, the value of "p" will be "4".