" Tension in the ring is "(pi B_(0)^(2)r_(0)^(3)alpha z(1-alpha z))/(2L)

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)

If P(z) is a variable point and A(z_(1)) and B(z_(2)) are the two fixed points in the argand plane |z-z_(0)|=|(bar(boldsymbol alpha)z_(0)+alphabar(z)_(0)+r)/(2| alpha|))

Intercept made by the circle zbar(z)+alphabar(z)+bar(alpha)z+r=0 on the real axis on complex plane,is (a) sqrt(alpha+alpha)-r)(b)sqrt(alpha+alpha)-2r)( c) sqrt(alpha+alpha)+r)(d)sqrt((alpha+alpha)^(2)-4r)

If P(z) is a variable point and A(z_(1)) and B(z_(2)) are the two fixed points in the argand plane (i)arg ((z-z_(1))/(z-z_(2)))=+-(pi)/(2) (ii) arg((z-z_(1))/(z-z_(2)))=0 or alpha

If Z+alpha|Z-1|+2i=0 , then find the sum of maximum and minimum values of alpha .( alpha in R )

If for some alpha in R, the lines L_1 : (x + 1)/(2) = (y-2)/(-1) = ( z -1)/(1) and L_2 : (x + 2)/(alpha) = (y +1)/(5 - alpha) = (z + 1)/(1) are coplanar , then the line L_2 passes through the point :