Question

(i) Lines 2x - by + 5 = 0 and ax + 3y = 2 are parallel to each other. Find the relation connecting a and b.

(ii) Lines mx + 3y + 7 = 0 and 5x - ny - 3 = 0 are perpendicular to each other. Find the relation connecting m and n.
$\left[4Marks\right]$

Answer 1

(i) 2x - by + 3 = 0

by = 2x + 3

y =
$\left[1Mark\right]$

Slope of this line =

ax + 3y = 2

3y = -ax + 2

y =
$\left[0.5Marks\right]$

Slope of this line =

Since, the lines are parallel, so the slopes of the two lines are equal.

$\left[0.5Marks\right]$

(ii) mx + 3y + 7 = 0

3y = -mx - 7

y =
$\left[0.5Marks\right]$

Slope of this line =

5x - ny - 3 = 0

ny = 5x - 3

y =
$\left[0.5Marks\right]$

Slope of this line =

Since, the lines are perpendicular; the product of their slopes is -1.

$\left[1Mark\right]$