The curve described parametrically by `x=t^2+t+1` , and `y=t^2-t+1` represents. a pair of straight lines (b) an ellipse a parabola (d) a hyperbola

The curve described parametrically by x=t^(2)+t+1,y=t^(2)-t+1 represents :

Show that the curve whose parametric coordinates are x=t^(2)+t+l,y=t^(2)-t+1 represents a parabola.

The curve represented by x=2(cos t+sin t) and y=5(cos t-sin t) is

The coordinates of the focus of the parabola described parametrically by x=5t^2+2, y=10t+4 are

If y = f(x) defined parametrically by x = 2t - |t - 1| and y = 2t^(2) + t|t| , then

A curve in the co-ordinate plane is given by the parametric equation x = t^2+t+ 2 and y=t^2- t+2 where t ge 0 . The number of straight lines passing through the point (2, 2) which are tangent to the curve is/are

IF t is a parameter, then x = a(t + (1)/(t)) and y = b(t - (1)/(t)) represents