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

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

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

The locus of the represented by x = t^ 2 + t + 1 , y = t ^ 2 - t + 1 is

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

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

The parametric equations x=(2a(1-t^(2)))/(1+t^(2)) and y=(4at)/(1+t^(2)) represents a circle whose radius is

A curve parametrically given by x=t+t^(3)" and "y=t^(2)," where "t in R." For what vlaue(s) of t is "(dy)/(dx)=(1)/(2) ?

A curve parametrically given by x=t+t^(3)" and "y=t^(2)," where "t in R." For what vlaue(s) of t is "(dy)/(dx)=(1)/(2) ?

A curve parametrically given by x=t+t^(3)" and "y=t^(2)," where "t in R." For what vlaue(s) of t is "(dy)/(dx)=(1)/(2) ?

A curve is defined parametrically be equations x=t^2a n dy=t^3 . A variable pair of perpendicular lines through the origin O meet the curve of Pa n dQ . If the locus of the point of intersection of the tangents at Pa n dQ is a y^2=b x-1, then the value of (a+b) is____