# Reduce the Following Equation to the Normal Form and Find P and α in X + Y + √ 2 = 0 . - Mathematics

Reduce the following equation to the normal form and find p and α in $x + y + \sqrt{2} = 0$.

#### Solution

$x + y + \sqrt{2} = 0$

$\Rightarrow - x - y = \sqrt{2}$

$\Rightarrow - \frac{x}{\sqrt{\left( - 1 \right)^2 + \left( - 1 \right)^2}} - \frac{y}{\sqrt{\left( - 1 \right)^2 + \left( - 1 \right)^2}} = \frac{\sqrt{2}}{\sqrt{\left( - 1 \right)^2 + \left( - 1 \right)^2}} \left[\text { Dividing both sides by } \sqrt{\left( \text { coefficient of x } \right)^2 + \left( \text { coefficient of y } \right)^2} \right]$

$\Rightarrow - \frac{x}{\sqrt{2}} - \frac{y}{\sqrt{2}} = 1$

This is the normal form of the given line, where p = 1,

$cos\alpha = - \frac{1}{\sqrt{2}}$

$\sin\alpha = - \frac{1}{\sqrt{2}}$

$\Rightarrow \alpha = {225}^\circ \left[ \because \text { The coefficent of x and y are negative . So, } \alpha \text { lies in third quadrant } \right]$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 23 The straight lines
Exercise 23.9 | Q 2.2 | Page 72