[x+2y-4=0----(i)],[2x+4y-12=0----(ii)]

Find the parametric representation of circles : (i) x^(2) + y^(2) + 12x - 4y - 1 = 0 (ii) x^(2) + y^(2) + 2gx + 2fy + c = 0 .

Find the number of possible common tangents of following pairs of circles (i) x^(2)+y^(2)-14x+6y+33=0 x^(2)+y^(2)+30x-2y+1=0 (ii) x^(2)+y^(2)+6x+6y+14=0 x^(2)+y^(2)-2x-4y-4=0 (iii) x^(2)+y^(2)-4x-2y+1=0 x^(2)+y^(2)-6x-4y+4=0 (iv) x^(2)+y^(2)-4x+2y-4=0 x^(2)+y^(2)+2x-6y+6=0 (v) x^(2)+y^(2)+4x-6y-3=0 x^(2)+y^(2)+4x-2y+4=0

Find the number of possible common tangents of following pairs of circles (i) x^(2)+y^(2)-14x+6y+33=0 x^(2)+y^(2)+30x-2y+1=0 (ii) x^(2)+y^(2)+6x+6y+14=0 x^(2)+y^(2)-2x-4y-4=0 (iii) x^(2)+y^(2)-4x-2y+1=0 x^(2)+y^(2)-6x-4y+4=0 (iv) x^(2)+y^(2)-4x+2y-4=0 x^(2)+y^(2)+2x-6y+6=0 (v) x^(2)+y^(2)+4x-6y-3=0 x^(2)+y^(2)+4x-2y+4=0

The graphical representation of x+2y-4= 0 and 2x+4y-12=0 will be

Find two solutions for each (i) 4x + 3y = 12 (ii) 2x + 5y = 0 (ii) 3y + 4 = 0

Classify the following pairs of lines as coincident, parallel, perpendicular or intersecting : (i) 6x+14y-16=0 , 12x+28y-32=0 (ii) 3x-4y=8 , 3x+4y=11 (iii) 5x-2y=7 , 2y-5x=-7 (iv) 4x+7y=19 , 7x-4y=-2 (v) x-2y=7 , 4y-2x=13

The equation of the directrix of the parabola x^(2) - 4x - 8y + 12 = 0 is (i) y = 0 (ii) x - 1 = 0 (iii) y+ 1 = 0 (iv) x + 1 = 0

The vertex of the parabola x^(2)+8x+12y+4=0 is (i) (-4,1) (ii) (4,-1)( iii) (-4,-1)

The vertex of the parabola x^2+8x+12y+4=0 is (i) (-4,1) (ii) (4,-1) (iii) (-4,-1)

(i) x^(2)-7x+12=0 (ii) y^(2)+y-12=0