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

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=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+i sqrt(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 argand plane is

If x = (2at)/(1 + t^2) , y = (a(1-t^2) )/(1 + t^2) , where t is a parameter, then a is

If the co-ordinates of a point P are x = at^(2) , y = a sqrt(1 - t^(4)) , where t is a parameter , then the locus of P is a/an

Find the equation to the locus represented by x=(2+t+1)/(3t-2), y=(t-1)/(t+1) wher t is variable parameter.

IF x=t^2+2t,y=t^3-3t , where t is a parameter then show that, (d^2y)/(dx^2)=3/(4(t+1)) .

Show that equations x = 5 * (1 - t^(2))/(1 + t^(2)), y = 6 * (t)/(1 + t^(2) ) where t is a variable parameter, define an ellipse . Find its eccentricity .