Q.6 The curve represented by `R((1)/(z))=c` (where `c!=0` ) is a/an

Form the differential equation of the family of curves represented c(y+c)^(2)=x^(3) where c is a parameter.

If z=a+ib, |z|=1 and b ne 0, show that z can be represented as z=(c+i)/(c-i) where c is a real number.

Let C_(1) be the curve represented by (2z + i)/(z-2) is purely imaginary, and C_(2) be the curve represented by arg ((z+i)/(z+1))=(pi)/(2) . Let m = slope of the common chord of C_(1) and C_(2) , then |m| is equal to ___________.

The differential equation of the family of curves represented by y^3= cx+ c^3+ c^2-1 ,where c is an arbitrary constant is of :

Form the differential equation of the family of curves represented c(y+c)^(2)=x^(3), where is a parameter.

The curve represented by the equation sqrt(px)+sqrt(qy)=1 where p,q in R,p,q>0 is a circle (b) a parabola an ellipse (d) a hyperbola

From the differential equation of the family of curves represented by y = a cos (bx + c) where a, b, c are the arbitrary constants.

Which one of the following is the differential equation that represents the family of curves y=(1)/(2x^(2)-c) where c is an arbitrary constant ?

The largest value of r for which the region represented by the set {omega in C/| omega-4-i|<=r} is contained in the region represented by the set {z in C/|z-1|<=|z+i|}, is equal to

Let PQRS be a square with the vertices P,Q lying on the curve C_(1):y=x^(2) and R, s lying on the curve C_(2):y=x+8. If the coordinates of P and Q be represented by (x_(1),y_(1)) and (x_(2),y_(2)), then algebraic sum of all possible abscissae of P is: