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Grade 12th passAnalytical Geometry

Show that the following equation represents a pair of lines find also the angle between them 6x2+13xy+6y2+8x+7y+2=0

Profile image of Rajeev
6 Years agoGrade 12th pass
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2 Answers

Profile image of Arun
6 Years ago
The angle between pair of straight lines represented by ax^2 + 2hxy + by^2 + 2gx + 2fy +c =0 is given by --------1
tanthetha= | (2( h^2 – ab) ^ ½ ) / (a+b) |
comparing the equation given in question with 1
a=6 ; b= 6 ; h = 13/2 ; g=4; f= 7/2 ; c= 2;
tanthetha = | (2( 13/2 ^2 – 6 . 6 ) ^ ½ ) / (6 + 6) |
tanthetha = | (2( 6.25 ) ^ ½ ) / 12 |
tanthetha=| 5/12 |
Hence thetha = tan-1 5/12
 
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