If the equation `|z-a|+|z-b|=3` represents an ellipse and `a ,b in C ,w h e r ea` is fixed, then find the locus of `bdot`

If w=z/[z-(1/3)i] and |w|=1, then find the locus of z

Statement 1 : If aa n db are real numbers and c >0, then the locus represented by the equation |a y-b x|=csqrt((x-a)^2+(y-b)^2) is an ellipse. Statement 2 : An ellipse is the locus of a point which moves in a plane such that the ratio of its distances from a fixed point (i.e., focus) to that from the fixed line (i.e., directrix) is constant and less than 1.

If the roots of the equation x^3+P x^2+Q x-19=0 are each one more that the roots of the equation x^3-A x^2+B x-C=0,w h e r eA ,B ,C ,P ,a n dQ are constants, then find the value of A+B+Cdot

If one root of the equation z^2-a z+a-1=0i s(1+i),w h e r ea is a complex number then find the root.

If z=x+i y , then he equation |(2z-i)/(z+1)|=m represents a circle, then m can be (a) 1/2 b. 1 c. 2 d. 3

Variable complex number z satisfies the equation |z-1+2i|+|z+3-i|=10 . Prove that locus of complex number z is ellipse. Also, find the centre, foci and eccentricity of the ellipse.

P represents the variable complex number z find the locus of z if : Re((z+1)/(z+i))=1

If the complex numbers xa n dy satisfy x^3-y^3=98 ia n dx-y=7i ,t h e nx y=a+i b ,w h e r ea ,b , in Rdot The value of (a+b)//3 equals ______.

If x=c y+b z ,y=a z+c x ,z=bx+a y ,w h e r ex ,y ,z are not all zeros, then find the value of a^2+b^2+c^2+2a b c dot

Find the value of the determinant |b cc a a b p q r1 1 1|,w h e r ea ,b ,a n dc are respectively, the pth, qth, and rth terms of a harmonic progression.