Transform to parallel axes through the point (1,-2) the equation `y^2 - 4x + 4y + 8 = 0`.

The equation x^(2)+2xy+4=0 is transformed to the parallel axes through the point (6, lambda) . For what value of lambda its new form passes through the new origin ?

The ellipse x^2+""4y^2=""4 is inscribed in a rectangle aligned with the coordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is (1) x^2+""16 y^2=""16 (2) x^2+""12 y^2=""16 (3) 4x^2+""48 y^2=""48 (4) 4x^2+""64 y^2=""48

The ellipse x^2+ 4y^2 = 4 is inscribed is a rectangle alligned with the co-ordinate axes, which in turn is inscribed in another ellipse that passes through the point (4, 0). Then the equation of the ellipse is :

Transform the equation x^(2)-3xy+11x-12y+36=0 to parallel axes through the point (-4, 1) becomes ax^(2)+bxy+1=0 then b^(2)-a=

Transform the equation x^(2)-3xy+11x-12y+36=0 to parallel axes through the point (-4, 1) becomes ax^(2)+bxy+1=0 then b^(2)-a=

Find the equation of the line passing through the point of intersection of the lines 4x + 7y-3 = 0 and 2x -3y +1=0 that has equal intercepts on the axes.

Find the equation of plane passing through the point (1,4,-2) and parallel to the plane 2x-y+3z=0

If a circle is concentric with the circle x^(2)+y^(2)-4x-6y+9=0 and passes through the point (-4,-5) then its equation is

The asymptotes of the hyperbola centre of the point (1, 2) are parallel to the lines 2x+3y=0 and 3x+2y=0 . If the hyperbola passes through the points (5, 3) , show that its equation is (2x+3y-8)(3x+2y+7)=154

Find the equation of the circle passing through the points of intersection of the circles x^2 + y^2 - 2x - 4y - 4 = 0 and x^2 + y^2 - 10x - 12y +40 = 0 and whose radius is 4.