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AP EAMCET202018 Sep 2020Morning ShiftMathematicsStraight LinesActual

A straight line is drawn through the point (A(1,2) ) such that its point of intersection with the straight line (x+y=4 ) is at a distance ( 6 3 ) from the given point ' (A ) '. Find the angle which the line makes with the positive direction of (X )-axis.

Options

  1. A( =15^ ) and (75^ )
  2. B( =75^ ) and (45^ )
  3. C( =45^ ) and (60^ )
  4. D( =60^ ) and (30^ )

Correct answer

A. ( =15^ ) and (75^ )

Step-by-step solution

Let the angle of inclination of line ( ), and as passed through point (A(1,2) ), so equation of line is ( x-1 = y-2 = 6 3 ) ( ) General point on the line is (P (1 6 3 , 2 6 3 ) ) Let the point (P ) on the straight line (x+y=4 ), so ( aligned & 3 6 3 ( + )=4 & 6 3 ( + )=1 aligned ) On squaring both sides, we get ( gathered 2(1+ 2 )=3 2 = 1 2 2 =30^ and 150^ =15^ and 75^ gathered )

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