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Manipal MET2014MathematicsThree Dimensional Geometry

The equations of the lines passing through the point (1,0) and at a distance 3 2 from the origin are

Options

  1. A3 x+y- 3 =0, 3 x-y- 3 =0
  2. B3 x+y+ 3 =0, 3 x-y+ 3 =0
  3. Cx+ 3 y- 3 =0, x- 3 y- 3 =0
  4. DNone of the above

Correct answer

A. 3 x+y- 3 =0, 3 x-y- 3 =0

Step-by-step solution

Let slope of a line be m . Now, the equation of a line passing through (1,0) is aligned y-0 & =m(x-1) m x-y-m & =0 aligned Distance from origin = 3 2 array ll & |-m| 1+m^2 = 3 2 & 4 m^2=3 (1+m^2 ) & m^2=3 & m= 3 array Equations of lines are array lrl & 3 x-y- 3 & =0 and & - 3 x-y+ 3 & =0 & 3 x-y- 3 =0 and & 3 x+y- 3 =0 array

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