The name of the curve described parametrically by the equations x = t 2 + t + 1 ,   y = t 2 - t + 1 , is

Step-by-step solution

Here, we are having x = t 2 + t + 1 ,   y = t 2 - t + 1 , On subtracting y from x , we get x - y = t 2 + t + 1 - t 2 - t + 1 ⇒ x - y = 2 t or t = x   -   y 2 , On putting the value of t , in x , we get x   =   x   -   y 2 2   +   x   -   y 2   +   1 , On further simplification, we get x = x 2   -   2 x y   +   y 2 4 + x   -   y 2 + 1 , ⇒ 4 x = x 2 - 2 x y + y 2 + 2 x - 2 y + 4 , Final equation, we get as x 2 -