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+8h-16 b=0` (b) `a-8h+16 b=0` `a-6h+9b=0` (d) `a+6h+9b=0`

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

Show that the pairs of straight lines 2x^2+6x y+y^2=0 and 4x^2+18 x y+y^2=0 have the same set of angular bisector.

If the equation x^2+b x-a=0"and" x^2-a x+b=0 have a common root, then a. a+b=0 b. a=b c. a-b=1 d. a+b=1

If the pair of straight lines a x^2+2h x y+b y^2=0 is rotated about the origin through 90^0 , then find the equations in the new position.

Through a point A on the x-axis, a straight line is drawn parallel to the y-axis so as to meet the pair of straight lines a x^2+2h x y+b y^2=0 at B and Cdot If A B=B C , then (a) h^2=4a b (b) 8h^2=9a b (c) 9h^2=8a b (d) 4h^2=a b

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 gradient of one of the lines x^2+h x y+2y^2=0 is twice that of the other, then h=

The distance between the two lines represented by the equation 9x^2-24xy+16y^2-12x+16y-12=0 is

The equation of a line which is parallel to the line common to the pair of lines given by 6x^2-x y-12 y^2=0 and 15 x^2+14 x y-8y^2=0 and at a distance of 7 units from it is (a) 3x-4y=-35 (b) 5x-2y=7 (c) 3x+4y=35 (d) 2x-3y=7

Two straight lines are perpendicular to each other. One of them touches the parabola y^2=4a(x+a) and the other touches y^2=4b(x+b) . Their point of intersection lies on the line. (a) x-a+b=0 (b) x+a-b=0 (c) x+a+b=0 (d) x-a-b=0