Find c if the line `ax + by + c = 0` is a diameter of the circle `x^2 + y^2 =1`.

If the line x+2b y+7=0 is a diameter of the circle x^2+y^2-6x+2y=0 , then find the value of b .

If the straight line ax + by = 2 ; a, b!=0 , touches the circle x^2 +y^2-2x = 3 and is normal to the circle x^2 + y^2-4y = 6 , then the values of 'a' and 'b' are ?

If the circle x^2+y^2 +4x+22y + c = 0 bisects the circumference of the circle x^2 + y^2-2x + 8y-d = 0 ,then (c+d) is equal to

The equation of one of the diameters of the circle x^2+y^2 - 6x + 2y =0 is:

One of the diameters of the circle x^2+y^2-12x+4y+6=0 is given by

If the lines 2x + 3y + 1 = 0 and 3x - y-4 = 0 lie along two diameters of a circle of circumference 10 pi , then the equation of circle 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 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

Determine the equation of the circle whose diameter is the chord x + y = 1 of the circle x^2 +y^2= 4 .

Find the equation of the circle through points of intersection of the circle x^2 + y^2 -2x - 4y + 4 =0 and the line x + 2y = 4 which touches the line x + 2y = 0 .

Find the equation of a circle, which touches the line x+ y = 5 at the point (-2, 7) and cuts the circle x^2+ y^2+ 4x - 6y +9 =0 orthogonally.