Question

i want solution of both

Answer 1

1) x^2-5xy+6y^2
orx^2-3xy-2xy+6y^2=0
or x (x-3y)-2y (x-3y) =0
or (x-3y)(x-2y)=0
so x-3y= 0 and x-2y = 0
but this is not their in the option
so for 3) Tick "d" option

for 4)

The  gradint of  one of the line of ax2+2hxy+by2 =0 is twice that of the other,

Here,gradient refers to the slope of the line.

And further,in pair of straight lines,m1+m2=-2h/b and m1m2=a/b,where m1 and m2 are the slopes of the two lines represented by the equation ax2+2hxy+by2=0.

Let m1=m,then m2=2m1=2m.

Now,m+2m=-2h/b

→3m==-2h/b

→m=-2h/3b...............................(1)

Also,(m)(2m)=a/b

→2m2=a/b

→m2=a/2b

→(-2h/3b)2=a/2b..............................from (1)

→4h2/9b2 =a/2b

→8h2=9ab

So,option (A) is the correct answer