Misc 13 - Equation of line passing through origin, making angle - Angle between two lines

  1. Chapter 10 Class 11 Straight Lines
  2. Serial order wise
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Misc 13 Show that the equation of the line passing through the origin and making an angle with the line y = mx + c is / = ( )/(1 ) . Let OP be the line passing through origin Let PQ be the line y = mx + c Whose slope is m and makes an angle with line OP We need to show equation line OP is / = ( )/(1 ) We know that equation of line passing through point(x1, y1) & having slope m is (y y1) = m(x x1) Let m1 be the slope of line OP Equation of a line OP passing through origin (0, 0) with slope m1 (y 0) = m1(x 0) y = m1x Now we need to find slope (i.e. m1) of line OP It is given that line OP makes an angle with line PQ y = mx + c Angle between two line whose slope are m1 & m2 is tan = |( _2 _1)/(1 + _2 _1 )| Angle between line OP & PQ is tan = |( _1 )/(1 + _1 )| |( _1 )/(1 + _1 )| = tan ( _1 )/(1 + _1 ) = tan So, ( _1 )/(1 + _1 ) = tan & ( _1 )/(1 + _1 ) = tan Hence, m1 = ( + tan )/(1 m tan ) and m1 = ( tan )/(1 + m tan ) m1 = ( tan )/(m m tan ) Putting value of m1 in (1) y = ( tan )/(m m tan ) / = ( tan )/(m m tan ) Hence proved

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