`|[x^2+y^2+1,x^2+2y^2+3,x^2+3y^2+4],[y^2+2,2y^2+6,3y^2+8],[y^2+1,2y^2+3,3y^2+4]|`=`x^2y^2`

The locus of the foot of perpendicular drawn from the centre of the ellipse x^2+""3y^2=""6 on any tangent to it is (1) (x^2-y^2)^2=""6x^2+""2y^2 (2) (x^2-y^2)^2=""6x^2-2y^2 (3) (x^2+y^2)^2=""6x^2+""2y^2 (4) (x^2+y^2)^2=""6x^2-2y^2

The locus of the foot of perpendicular drawn from the centre of the ellipse x^2+""3y^2=""6 on any tangent to it is (1) (x^2-y^2)^2=""6x^2+""2y^2 (2) (x^2-y^2)^2=""6x^2-2y^2 (3) (x^2+y^2)^2=""6x^2+""2y^2 (4) (x^2+y^2)^2=""6x^2-2y^2

Identify the type of conic section for each of the equations 1. 2x^(2) -y^(2) = 7 2. 3x^(2) +3 y^(2) -4x + 3y + 10 =0 3. 3x^(2) + 2y^(2) = 14 4. x^(2) + y^(2) + x-y=0 5. 11x^(2) -25y^(2) -44x + 50y - 256 =0 6. y^(2) + 4x + 3y + 4=0

The equation of the circle whose diameter is the common chord of the circles; x^2+y^2+3x+2y+1=0 and x^2+y^2+3x+4y+2=0 is: x^2+y^2+8x+10 y+2=0 x^2+y^2-5x+4y+7=0 2x^2+2y^2+6x+2y+1=0 None of these

From the sum of x^2+3y^2-6x y ,2x^2-y^2+8x y , y^2+8 and x^2-3x y\ subtract -3x^2+4y^2-x y+x-y+3.

From the sum of x^2+3y^2-6x y ,2x^2-y^2+8x y , y^2+8 and x^2-3x y\ subtract -3x^2+4y^2-x y+x-y+3.

Subtract: x^2y-4/5x y^2+4/3x y\ from 2/3x^2y+3/2x y^2-1/3x y

The equation of the transvers and conjugate axes of a hyperbola are, respectively, x+2y-3=0 and 2x-y+4=0 , and their respective lengths are sqrt(2) and 2sqrt(3)dot The equation of the hyperbola is 2/5(x+2y-3)^2-3/5(2x-y+4)^2=1 2/5(x-y-4)^2-3/5(x+2y-3)^2=1 2(2x-y+4)^2-3(x+2y-3)^2=1 2(x+2y-3)^2-3(2x-y+4)^2=1