First slide

Equation of line in Straight lines

Question

$The straight lines represented by (y - m x)^{2} = a^{2} (1 + m^{2}) and (y - n x)^{2} = a^{2} (1 + n^{2}) form a$

Moderate

A

rectangle
B

rhombus
C

trapezium
D

none of these

Solution

$The straight lines represented by (y - m x)^{2} = a^{2} (1 + m^{2}) are$
$y - m x = \pm a \sqrt{1 + m^{2}}$
$i.e., y - m x = a \sqrt{1 + m^{2}} - - - - - (1)$
$and y - m x = - a \sqrt{1 + m^{2}} - - - - - - (2)$
$\begin{array}{l} Similarly, the straight lines represented by (y - n x)^{2} = a^{2} (1 + n^{2}) are \end{array}$
$y - n x = a \sqrt{1 + n^{2}} - - - - (3)$
$and y - n x = - a \sqrt{1 + n^{2}} - - - - (4)$
Since the lines (1) and (2) are parallel, the distance between them is
$|\frac{a \sqrt{1 + m^{2}} + a \sqrt{1 + m^{2}}}{\sqrt{1 + m^{2}}}| = | 2 a |$
$\begin{array}{rcl} S i m i l a r l y, t h e l i n e s (i i i) a n d (i v) a r e p a r a l l e l l i n e s a n d t h e d i s \tan c e b e t w e e n t h e m i s |2 a| . \\ S i n c e t h e d i s \tan c e s b e t w e e n p a r a l l e l l i n e s a r e t h e s a m e, t h e f o u r l i n e s f o r m a r h o m b u s . \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App