The straight lines represented by `x^2+m x y-2y^2+3y-1=0` meet at (a)`(-1/3,2/3)` (b) `(-1/3,-2/3)` (c)`(1/3,2/3)` (d) none of these

for parabola x^2+y^2+2xy?6x?2y+3=0, the focus is (a) (1,-1) (b) (-1,1) (c) (3,1) (d) None of these

The separate equations of the lines represented by the line equation 8(x-1)^(2)+10(x-1)(y-3)-3(y-3)^(2)=0 are

Show that the straight lines : x-y-1=0 , 4x+3y=25 and 2x-3y+1=0 are concurrent.

If the straight lines x+y-2-0,2x-y+1=0 and a x+b y-c=0 are concurrent, then the family of lines 2a x+3b y+c=0(a , b , c) are nonzero) is concurrent at (a) (2,3) (b) (1/2,1/3) (c) (-1/6,-5/9) (d) (2/3,-7/5)

The area {(x,y);x^(2)<=y<=sqrt(x)} is equal to (1)/(3) b.(2)/(3) c.(1)/(6) d.none of these

If the equation (4a-3)x^(2)+ay^(2)+6x-2y+2=0 represents a circle,then its centre is a.(3,-1) b.(3,1) c.(-3,1) d.none of these

The co-ordinates of the centre of the hyperbola,x^(2)+3xy+3y^(2)+2x+3y+2=0 is (-1,0)( b) (1,0)(-1,1)(d)(1,-1)

The area of the region bounded by 1-y^(2)=|x| and |x|+|y|=1 is (a)1/3(b)2/3(c)4/3(d)1

If xy-log_(e)y=1 satisfies the equation x(yy_(2)+y_(1)^(2))-y_(2)+lambda yy_(1)=0, then lambda=-3 (b) 1 (c) 3 (d) none of these