Question

The condition for the pair of equation ax+by+c=0 and px+qy+r=0 to represent coinciding line is​

Answer 1

Answer:

a/p = b/q = c/r

is the condition for coinciding lines

Answer 2

Answer:

$\frac{a}{p} = \frac{b}{q} = \frac{c}{r}$ is the required condition for the given  pair of equation.

Step-by-step explanation:

Explanation:

Given , ax + by + c = 0 and

px + qy + r = 0

• Coinciding line - Coincident lines are two lines that lie on top of each other. If the slopes and intercepts of two lines are the same, they are coincident.

• As we know ,  condition for the pair of equation $a_1x + b_1 y +c_1 = 0$ and    $a_2x + b_2 + c_2 = 0$ to represent coinciding line

              $\frac{a_1}{a_2}$ = $\frac{b_1}{b_2}$  = $\frac{c_1}{c_2}$

• Therefore , we have from the given question , $a_1 = a$ ,$a_2 = p$ ,$b_1 = b$ ,$b_2 = q$ , $c_1 = c and \ c_2 = r$ .
• So , the condition for the pair of equation  ax + by + c = 0

           and  px + qy + r = 0  

         ⇒$\frac{a}{p} = \frac{b}{q} = \frac{c}{r}$

Final answer:

Hence , $\frac{a}{p} = \frac{b}{q} = \frac{c}{r}$ is the condition to represent coinciding line .

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