Advertisement Remove all ads

Find the Equation of a Line Which is Perpendicular to the Line \[\Sqrt{3}X - Y + 5 = 0\] and Which Cuts off an Intercept of 4 Units with the Negative Direction Of Y-axis. - Mathematics

Answer in Brief

Find the equation of a line which is perpendicular to the line \[\sqrt{3}x - y + 5 = 0\] and which cuts off an intercept of 4 units with the negative direction of y-axis.

Advertisement Remove all ads

Solution

The line perpendicular to \[\sqrt{3}x - y + 5 = 0\] is \[x + \sqrt{3}y + \lambda = 0\].

It is given that the line \[x + \sqrt{3}y + \lambda = 0\]  cuts off an intercept of 4 units with the negative direction of the y-axis.
This means that the line passes through \[\left( 0, - 4 \right)\].

\[\therefore 0 - \sqrt{3} \times 4 + \lambda = 0\]

\[ \Rightarrow \lambda = 4\sqrt{3}\]

Substituting the value of \[\lambda\], we get 

\[x + \sqrt{3}y + 4\sqrt{3} = 0\], which is the equation of the required line.

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 23 The straight lines
Exercise 23.12 | Q 5 | Page 92
Advertisement Remove all ads

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×