Two pairs of straight lines have the equations `y^2+x y-12 x^2=0` and `a x^2+2h x y+b y^2=0` . One line will be common among them if. (a)`a+8h-16 b=0` (b) `a-8h+16 b=0` (c)`a-6h+9b=0` (d) `a+6h+9b=0`

Two pairs of straight lines have the equations y^(2)+xy-12x^(2)=0andax^(2)+2hxy+by^(2)=0 . One line will be common among them if

The equations a^2x^2+2h(a+b)xy+b^2y^2=0 and ax^2+2hxy+by^2=0 represent.

If the pairs of lines ax^2+2hxy+by^2=0 and a'x^2+2h'xy+b'y^2=0 have one line in common, then (ab'-a'b)^2 is equal to

The condition that one of the straight lines given by the equation ax^(2)+2hxy+by^(2)=0 may coincide with one of those given by the equation a'x^(2)+2h'xy+b'y^(2)=0 is

Let the equation of circle is x^(2) + y^(2) - 6x - 4y + 9 = 0 . Then the line 4x + 3y - 8 = 0 is a

The graphs of the equations 6x-2y+9=0 and 3x-y+12=0 lines which are

If 2 is a root of the equation x^2+b x+12=0 and the equation x^2+b x+q=0 has equal roots, then q= (a) 8 (b) -8 (c) 16 (d) -16

The condition that one of the straight lines given by the equation a x^2+2h x y+b y^2=0 may coincide with one of those given by the equation a^(prime)x^2+2h^(prime)x y+b^(prime)y^2=0 is (a b^(prime)-a^(prime)b)^2=4(h a^(prime)-h^(prime)a)(b h^(prime)-b^(prime)h) (a b^(prime)-a^(prime)b)^2=(h a^(prime)-h^(prime)a)(b h^(prime)-b^(prime)h) (h a^(prime)-h^(prime)a)^2=4(a b^(prime)-a^(prime)b)(b h^(prime)-b^(prime)h) (b h^(prime)-b^(prime)h)^2=4(a b^(prime)-a^(prime)b)(h a^(prime)-h^(prime)a)

If the lines x +3y -9 = 0, 4x + by -2 = 0 and 2x -y -4 = 0 are concurrent , the b is equal to

If one of the lines represented by the equation ax^(2)+2hxy+by^(2)=0 is coincident with one of the lines represented by a'x^(2)+2h'xy+b'y^(2)=0, then