The curve described parametrically by #x=t^2+t+1#, and #y=t^2-t+1# represents?

Question

A) a pair of straight lines
B) an ellipse
C) a parabola
D) a hyperbola

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Answer 1 · 2018-03-02T09:51:41

(C)

#{(x=t^2+1+t),(y=t^2+1-t):}#

Adding and subtracting both equations

#{(1/2(x+y)=t^2+1),(1/2(x-y) = t):}#

then making now the coordinates change

#{(u = 1/2(x+y)),(v=1/2(x-y)):}#

we get

#u = v^2+1# which is a parabola equation.