Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse: (i) x2+2y2−2x+12y+10=0 (ii) x2+4y2−4x+24y+31=0 (iii) 4x2+y2−8x+2y+1=0 (iv) 3x2+4y2−12x−8y+4=0 (v) 4x2+16y2−24x−32y−12=0 (vi) x2+4y2−2x=0

Find the centre, the lengths of the axes, eccentricity, foci of the fo

1.	Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse: (i) x2+2y2−2x+12y+10=0 (ii) x2+4y2−4x+24y+31=0 (iii) 4x2+y2−8x+2y+1=0 (iv) 3x2+4y2−12x−8y+4=0 (v) 4x2+16y2−24x−32y−12=0 (vi) x2+4y2−2x=0
Answer» Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse: (i) $x^{2} + 2 y^{2} - 2 x + 12 y + 10 = 0$ (ii) $x^{2} + 4 y^{2} - 4 x + 24 y + 31 = 0$ (iii) $4 x^{2} + y^{2} - 8 x + 2 y + 1 = 0$ (iv) $3 x^{2} + 4 y^{2} - 12 x - 8 y + 4 = 0$ (v) $4 x^{2} + 16 y^{2} - 24 x - 32 y - 12 = 0$ (vi) $x^{2} + 4 y^{2} - 2 x = 0$