The normal to a curve at P(x, y) meets the X-axis at G. If the distance of G from the origin is twice the abscissa of P then the curve is

The co-ordinate of a point on the auxiliary circle of the ellipse x² + 2y² = 4 corresponding to the point on the ellipse whose eccentric angle is 60$$^\circ$$ will be

The locus of the centre of a variable circle which always touches two given circles externally is

The points of intersection of two ellipses $${x^2} + 2{y^2} - 6x - 12y + 20 = 0$$ and $$2{x^2} + {y^2} - 10x - 6y + 15 = 0$$ lie on a circle. The centre of the circle is