Let `z=1-t+isqrt(t^2+t+2)`, where `t` is a real parameter.the locus of the z in argand plane is

Let z=1-t+isqrt(t^2+t+2) , where t is a real parameter.the locus of the z in arg and plane is

Let z=t^2-1+sqrt(t^4-t^2),where t in R is a parameter. Find the locus of z depending upon t , and draw the locus of z in the Argand plane.

A variable circle C has the equation x^2 + y^2 - 2(t^2 - 3t+1)x - 2(t^2 + 2t)y + t = 0 , where t is a parameter.The locus of the centre of the circle is

If |z+3i|+|z-i|=8 , then the locus of z, in the Argand plane, is

A curve is difined parametrically by x=e^(sqrtt),y=3t-log_(e)(t^(2)), where t is a parameter. Then the equation of the tangent line drawn to the curve at t = 1 is

If the imaginary part of (2z+1)/(i z+1) is -2 , then show that the locus of the point respresenting z in the argand plane is a straight line.

Let f (x) =x ^(2) +2x -t ^(2) and f(x)=0 has two root alpha (t ) and beta (t) (alpha lt beta) where t is a real parameter. Let I (t)=int _(alpha ) ^(beta)f (x) dx. If the maximum value of I (t) be lamda and | lamda| =p/q where p and q are relatively prime positive integers. Find the product (pq).

Find the locus of a complex number z=x +yi , satisfying the relation |z +i|=|z+ 2| . Illustrate the locus of z in the Argand plane

A=(sqrt(1-t^2)+t, 0) and B=(sqrt(1-t^2)-t, 2t) are two variable points then the locus of mid-point of AB is

If the coordinates of a vartiable point P be (t+(1)/(t), t-(1)/(t)) , where t is the variable quantity, then the locus of P is