The equations ax + by +c = 0 and dx + ey + c =0 represent the same straight line if

a. ad = be b. ac = bd c. bc = ad d. ab = de

Question

The equations ax + by +c = 0 and dx + ey + c =0 represent the
same straight line if
a ad = be b ac = bd c bc = ad d ab = de

Chetna Khanna · Accepted Answer

Given equations are ax + by + c = 0 and dx + ey + c = 0

Two equations represent same straight line if $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}}$

So, $\frac{a}{d} = \frac{b}{e} = \frac{c}{c}$

$\Rightarrow \frac{a}{d} = \frac{b}{e} = 1 \Rightarrow \frac{a}{d} = 1 and \frac{b}{e} = 1 \Rightarrow a = d and b = e or a \times b = d \times e \Rightarrow a b = d e$

Thus, the correct option is d.

The equations ax + by +c = 0 and dx + ey + c =0 represent the same straight line if a. ad = be b. ac = bd c. bc = ad d. ab = de

The equations ax + by +c = 0 and dx + ey + c =0 represent the same straight line if

a. ad = be b. ac = bd c. bc = ad d. ab = de