from a pointA (1,1),straight lines AL and AM are drawn at right angles to the pair of straight lines 3x2+7xy-2y2=0...then combined equation of AL and AM is............

Dear shivanshi

3x2+7xy-2y2=0

m1 + m2 = 7/2

 m1.m2 =-3/2

now let a line  a'(x-1)² + 2h'(x-1)(y-1) + b'(y-1)² =0   whose line is perpendicular to the these lines

 m3 = -1/m1

m4 = -1/m2

m3 + m4 = -(m1+m2)/m1m2  

 -2h'/b'         = 7/3

m3.m4  = -1/m1m1

   a'/b'     = -2/3

a'(x-1)² + 2h'(x-1)(y-1) + b'(y-1)² =0

or

a'/b' (x-1)² + 2h'/b' (x-1)(y-1) + (y-1)² =0

- 2/3  (x-1)² -7/3 (x-1)(y-1) + (y-1)² =0

or

   2 (x-1)² +7 (x-1)(y-1) +3 (y-1)² =0

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