# Show that the Line A2x + Ay + 1 = 0 is Perpendicular to the Line X − Ay = 1 for All Non-zero Real Values of A. - Mathematics

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

#### Solution

The given lines are
a2x + ay + 1 = 0         ... (1)
x − ay = 1                   ... (2)
Let $m_1 \text { and } m_2$  be the slopes of the lines (1) and (2).

$m_1 m_2 = - \frac{a^2}{a} \times \frac{1}{a}$

$= - 1$

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

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 23 The straight lines
Exercise 23.13 | Q 9 | Page 99