Let complex numbers `alpha and 1/alpha` lies on circle `(x-x_0)^2(y-y_0)^2=r^2 and (x-x_0)^2+(y-y_0)^2=4r^2` respectively. If `z_0=x_0+iy_0` satisfies the equation `2|z_0|^2=r^2+2` then `|alpha|` is equal to (a) `1/sqrt2` (b) `1/2` (c) `1/sqrt7` (d) `1/3`

Let complex numbers alpha and (1)/(alpha) lies on circle (x-x_(0))^(2)(y-y_(0))^(2)=r^(2) and (x-x_(0))^(2)+(y-y_(0))^(2)=4r^(2) respectively.If z_(0)=x_(0)+iy_(0) satisfies the equation 2|z_(0)|^(2)=r^(2)+2 then | alpha| is equal to (a) (1)/(sqrt(2))( b )(1)/(2)(c)(1)/(sqrt(7)) (d) (1)/(3)

Let complex numbers alpha " and " (1)/(bar alpha) lies on circles (x - x_(0))^(2) + (y- y_(0))^(2) = r^(2) and (x - x_(0))^(2) + (y - y_(0))^(2) = 4x^(2) , , respectively. If z_(0) = x_(0) + iy_(0) satisfies the equation 2 | z_(0) |^(2) = r^(2) + 2 , then |alpha| is equal to:

The number of common tangents of the circles x^(2)+y^(2)+4x+1=0 and x^(2)+y^(2)-2y-7=0 , is

If (x^2+y^2)dy=xydx and y(1)=1 . If y(x_0)=e then x_0 is equal to (A) sqrt(2)e (B) sqrt(3)e (C) 2e (D) e

Lines (x-1)/1 = (y-1)/2 = (z-3)/0 and (x-2)/0 = (y-3)/0 = (z-4)/1 are

The plane x+2y-z=4 cuts the sphere x^2+y^2+z^2-x+z-2=0 in a circle of radius (A) sqrt(2) (B) 2 (C) 1 (D) 3

The number of solutions of the system of equations: 2x+y-z=7,\ \ x-3y+2z=1,\ \ x+4y-3z=5 is (a) 3 (b) 2 (c) 1 (d) 0

A variable complex number z=x+iy is such that arg (z-1)/(z+1)= pi/2 . Show that x^2+y^2-1=0 .