Question 26.

26. If the equation ax​2 - 6xy + y2 + bx + cx + d = 0 represents a pair of lines whose slopes are m and m2, the value(s) of a is/are-
(A) a = -8
( B) a = 8
(C) a = 27
(D) a = -27

Dear Student,If the equation of pair of lines is Ax2 + 2Hxy + By2+2Gx + 2Fy + C = 0, thenSum of the slopes of two lines=-2HBProduct of the slopes of two lines=ABThe given equation is,ax2 - 6xy + y2 + bx + cy + d = 0    .....1Comparing 1 with standard equation, we get2H = -6; B = 1; A = aFrom the given question:m+m2=61m2+m-6=0m2+3m-2m-6=0m(m+3)-2(m+3)=0(m+3)(m-2)=0m=2 and -3Also,m×m2=aa=23 and -33a=8 and -27Regards

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