24. Two pairs of straight lines have the equations  y 2 + x y - 12 x 2 = 0   and   a x 2 + 2 h x y + b y 2 = 0 . One line will be common among them. If
(1) a = – 3(2h + 3b)                   ​(2) a = 8(h – 2b)              ​(3) a = 2(b + h)                     ​(4) a = – 3(b + h)

25. If one of the lines of  m y 2 + 1 - m 2   x y - m x 2 = 0  is a bisector of the angle between the lines xy = 0, then m is
​(1) 1                                           ​(2) 2             ​                    (3)  - 1 2                                  ​(4) –1

Dear Student,
Please find below the solution to the asked query:

25.We know that equation of bisector of ax2+2hxy+by2=0 isx2-y2a-b=xyhFor xy=0a=0, b=0, h=12x2-y20=xyhx2-y2=0y2=x2y=±xAbove equation must satisfymy2+1-m2xy-mx2=0Put y=x or y=-xmy2+1-m2y2-my2=0 or my2-1-m2y2-my2=0m+1-m2-m=0 m-1+m2-m=0m2=1 or m2=1m=±1  or m=±1i.e. m=1 or -1

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