Question

i want solution of a question

Answer 1

Given, 2x^2+7xy+3y^2+8x+14y+lambda = 0
since ax^2+2hxy+by^2+2gx+2fy+c = 0
abc+2fgh-af^2-bg^2-ch^2= 0
here , a=2 h = 7/2 b=3 g=4 f = 7 c= lambda
so 6lambda+ 2×7×4×(7/2) - 2 (7)^2-3 (4)^2-lambda (7/2)^2 = 0
or 6lambda + 196-98-48-49/4lambda = 0
or 25lambda/4 = 50
lambda = 200/25
lambda = 8 is right answer