Advertisement Remove all ads

Find the Equations to the Straight Lines Which Pass Through the Point (H, K) and Are Inclined at Angle Tan−1 M to the Straight Line Y = Mx + C. - Mathematics

Answer in Brief

Find the equations to the straight lines which pass through the point (h, k) and are inclined at angle tan−1 m to the straight line y = mx + c.

Advertisement Remove all ads

Solution

We know that the equations of two lines passing through a point \[\left( x_1 , y_1 \right)\] and making an angle \[\alpha\] with the given line y = m'x + c are \[y - y_1 = \frac{m^{\prime}\pm \tan\alpha}{1 \mp m^{\prime} \tan\alpha}\left( x - x_1 \right)\]

Here,

\[x_1 = h, y_1 = k, \alpha = \tan^{- 1} m, m^{\prime}= m\]

So, the equations of the required lines are

\[y - k = \frac{m + m}{1 - m^2}\left( x - h \right) and y - k = \frac{m - m}{1 + m^2}\left( x - h \right)\]

\[ \Rightarrow y - k = \frac{2m}{1 - m^2}\left( x - h \right) \text { and } y - k = 0\]

\[ \Rightarrow \left( y - k \right)\left( 1 - m^2 \right) = 2m\left( x - h \right)\text { and } y = k\]

Concept: Straight Lines - Equation of Family of Lines Passing Through the Point of Intersection of Two Lines
  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 23.18 | Q 4 | Page 124
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×