An ellipse with major axis `4` and minor axis `2` touches both the coordinate axes, then locus of its focus is

If a parabola whose length of latus rectum is 4a touches both the coordinate axes then the locus of its focus is

An ellipse of major axis 20sqrt(3) and minor axis 20 slides along the coordinate axes and always,remains confined in the 1^(st) quadrant. The locus of the centre of the ellipoe therefore descibes thearc of a circle.The length of this arc is

An ellipse is drawn by taking a diameter of the circle (x – 1)^2 + y^2 = 1 , as its semi-minor axis and a diameter of the circle x^2 + (y – 2)^2 = 4 as its semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is:

An ellipse is drawn by taking the diameter of the circle (x-1)^(2)+y^(2)=1 as semi-minor axis and a diameter of the circle x^(2)+(y-2)^(2)=4 as its semi-major axis. If the centre of the ellipse is the origin and its axes are the co-ordinate axes, then the equation of the ellipse is :

An ellipse drawn by taking a diameter of the circle (x-1)^(2)+y^(2)=1 as its semiminor axis and a diameter of the circle x^(2)+(y-2)^(2)=4 as its semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is

An ellipse is drawn by taking a diameter of the circle (x-1)^(2) + y^(2) = 1 as its semi-minor axis and a diameter of the the circle x^(2) +(y - 2)^(2) = 4 as its sem-major axis . If the centre of the ellipse is at the origin and its axes are the coordinate axes , then the equation of the ellipse is _