The circle `(x-a)^2 + (y-a)^2 = a^2` is rolled on the y-axis in the positive direction through one complete revolution. Find the equation of the circle in its new position.

The plane x-y-z=4 is rotated through an angle 90^(@) about its line of intersection with the plane x+y+2z=4 . Then the equation of the plane in its new position is

Find the parametric form of the equation of the circle x^2+y^2+p x+p y=0.

A line through the point A (2, 0), which makes an angle of 30^@ with the positive direction of x-axis is rotated about A in clockwise direction through an angle 15^@ . Then the equation of the straight line in the new position is :

A circle of radius 4 units touches the co-ordinate axes in the first quadrant. If the circle makes one complete roll on the x-axis along the positive direction of x-axis, find its equation in new position.

The circle x^2 + y^2+ 4x-7y + 12 = 0 cuts an intercept on y-axis equal to

Find the parametric equation of the circles : 2x^2 + 2y^2-5x-7y-3=0 .

Find the parametric equation of the circles : 3x^2 + 3y^2+4x-6y-4=0 .

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 the origin and its axes are the coordinate axes, then the equation of the ellipse is (1) 4x^2+""y^2=""4 (2) x^2+""4y^2=""8 (3) 4x^2+""y^2=""8 (4) x^2+""4y^2=""16

A circle of radius 5u n i t s touches the coordinate axes in the first quadrant. If the circle makes one complete roll on x-axis along he positive direction of x-axis , find its equation in new position.

A line passing through the point (3, 0) makes an angle 30^@ with the positive direction of x-axis. If this line is rotated through an angie of 15^@ in clockwise direction, find its equation in new position.