" (ii) "4x^(2)+y^(2)-8x+2y+1=0" I "

For the ellipse 4x ^(2)+ y ^(2) - 8x + 2y + 1=0, the focus and the equation of the directrix are respectively

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

Find the point to which the origin has to be shifted to eliminate x and y terms (to remove first degree terms) in the following equations (i) 4x^(2) + 9y^(2) - 8x + 36 y + 4 = 0 (ii) x^(2) + y^(2) - 2ax - 4ay + a^(2) = 0

Eccentricity of the ellipse 4x^(2)+y^(2)-8x+2y+1=0 is

Find the eccentricity, length of latus rectum, centre, foci, vertices and the equatioin to the dircctriccs of the hyperola. (i) 4x^(2)-5y^(2)-16x+10y+31=0 (ii) 5x^(2)-4y^(2)+20x+8y-4=0 (iii) 4(y+3)^(2)-9(x-2)^(2)=1 (iv) 4x^(2)-9y^(2)-8x-32=0

Equation of the parabola whose focus is centre of the circle " x^(2)+y^(2)=4x+6y " and whose directrix is the line " x-y=0 " , is A) " x^(2)+y^(2)+2xy-8x-12y+26=0 " B ) " x^(2)+y^(2)-2xy-8x-12y-26=0 " C) " x^(2)+y^(2)+2xy+8x+12y+26=0 " D) " x^(2)+y^(2)-2xy-8x-12y+26=0 "

Eccentricity of the ellipse 4x^(2)+y^(2)-8x-2y+1=0

Find the centre the lengths of the axes, eccentricity,foci of the following ellipse: 4x^(2)+y^(2)-8x+2y+1=0