Show that the line a2x + ay + 1 = 0 is perpendicular to the line x –

1.	Show that the line a2x + ay + 1 = 0 is perpendicular to the line x – ay = 1 for all non-zero real values of a.
Answer» Given: Line a²x + ay + 1 = 0 is perpendicular to the line x – ay = 1 To prove: The line a²x + ay + 1 = 0 is perpendicular to the line x – ay = 1 for all non-zero real values of a. Concept Used: Product of slope of perpendicular line is -1. Explanation: The given lines are a²x + ay + 1 = 0 … (1) x − ay = 1 … (2) Let m₁ and m₂ be the slopes of the lines (1) and (2). m₁m₂ = - \(\frac{a^2}{a}\times\frac{1}{a}\) = -1 Hence proved, line a²x + ay + 1 = 0 is perpendicular to the line x− ay = 1 for all non-zero real values of a.

Show that the line a2x + ay + 1 = 0 is perpendicular to the line x – ay = 1 for all non-zero real values of a.

Answer»

Given:

Line a²x + ay + 1 = 0 is perpendicular to the line x – ay = 1

To prove:

The line a²x + ay + 1 = 0 is perpendicular to the line x – ay = 1 for all non-zero real values of a.

Concept Used:

Product of slope of perpendicular line is -1.

Explanation:

The given lines are

a²x + ay + 1 = 0 … (1)

x − ay = 1 … (2)

Let m₁ and m₂ be the slopes of the lines (1) and (2).

m₁m₂ = - \(\frac{a^2}{a}\times\frac{1}{a}\) = -1

Hence proved, line a²x + ay + 1 = 0 is perpendicular to the line x− ay = 1 for all non-zero real values of a.