Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Show that the tangent of an angle between the lines x/a + y/b=1 and x/a-y/b=1 is 2ab/a^{2}-b^{2}

Show that the tangent of an angle between the lines \frac{x}{a}+\frac{y}{b}=1 and \frac{x}{a}-\frac{y}{b}=1 is  \frac{2ab}{a^{2}-b^{2}}

Answers (1)

Equation of line in intercept form \frac{x}{a}+\frac{y}{b}=1............(i) and \frac{x}{a}-\frac{y}{b}=1..............(ii)

  \frac{x}{a}+\frac{y}{b}=1

\frac{y}{b}=1-\frac{x}{a}

 y=b-\frac{b}{a}x

 y=\left (-\frac{b}{a} \right )x+b

  y=mx+b  Slope of equation 1 is m_{1}=-\frac{b}{a}

  Similarly for equation 2 ,  -\frac{y}{b}=1-\frac{x}{a}

 -y=b-\frac{b}{a}x

  y=\left (\frac{b}{a} \right )x-b

  y=\left (\frac{b}{a} \right )x+\left (-1 \right )b

Since, the above equation is in y=mx+b form 

  Slope of the equation 2 is m_{2}=\frac{b}{a}

 Let θ be the angle between the given two lines \tan \theta =\left | \frac{\left ( m_{1}-m_{2} \right )}{1+m_{1}m_{2}} \right |  

 Putting the values of m1 and m2 in above equation we get

\tan \theta =\left | \frac{-\frac{b}{a} -\frac{b}{a}}{1+\left ( -\frac{b}{a} \right )\left ( \frac{b}{a} \right )} \right |=\left | \frac{-2\left (\frac{b}{a} \right )}{1-\left (\frac{b^{2}}{a^{2}} \right )} \right |

=\left | -\frac{2ab}{a^{2}-b^{2}} \right |=\frac{2ab}{a^{2}-b^{2}}

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question