Question

If the lines representing the pair of equations $2x+3y-5=0$ and $8x+py+q=0$ are coincident, then

• A. $p=12,q=20$
• B. $p=12,q=-20$
• C. $p=-12,q=-20$
• D. $p=-12,q=20$

Answer 1

The correct option is B $p=12,q=-20$

Given equation:
$2x+3y-5=0$ and $8x+py+q=0$

Comparing the above equation with $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0,$ we get
$a_1=2,b_1=3,c_1=-5$
and $a_2=8,b_2=p,c_2=q$

We know that, if two lines are coincident, then
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
$\Rightarrow \frac{2}{8}=\frac{3}{p}=\frac{-5}{q}$
$\Rightarrow \frac{1}{4}=\frac{3}{p}=\frac{-5}{q}$

Solving $\frac{1}{4}=\frac{3}{p},$ we get
$\Rightarrow p=12$

Solving $\frac{1}{4}=\frac{-5}{q},$ we get
$\Rightarrow q=-20$