" (i) "x^(2)+2y^(2)-2x+12y+10=0

Find the centre the lengths of the axes, eccentricity,foci of the following ellipse: x^(2)+2y^(2)-2x+12y+10=0

Find the point at which is shifted such that the transformed equations of the following equations has no first degree term : (i) 2x^(2)+3y^(2)+4x-12y+10=0 (ii) x^(2)+y^(2)-xy-5x+4y+5=0

The vertices of the hyperbola x^(2) -3y^(2) +2x +12y +1=0 are

Find the equation of a circle which passes the centre of the circle x^(2)+y^(2)-6x =1 and concentric with the circle 2x^(2)+2y^(2)-8x +12y -1=0 .

Find the equation of a circle which passes the centre of the circle x^(2)+y^(2)-6x =1 and concentric with the circle 2x^(2)+2y^(2)-8x +12y -1=0 .

The radical centre of the circles x^(2) + y^(2)- 2x + 6y = 0 , x^(2) + y^(2) - 4x - 2y + 6 = 0 , x^(2) + y^(2) - 12x + 12y + 30 = 0 is

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 "

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