Question

The vertex of the parabola whose parametric equation is `x=t^2-t+1,y=t^2+t+1; t in R ,` is (1, 1) (b) (2, 2) `(1/2,1/2)` (d) `(3,3)`
A. (1,1)
B. (2,2)
C. (1/2, 1/2)
D. (3,3)

Answer 1

Correct Answer - A
(1) `x=t^(2)-t+1,y=t^(2)+t+1`
`orx+y=2(t^(2)+1)andy-x=2t`
`or(x+y)/(2)=1+((y-x)/(2))^(2)`
`or(y-x)^(2)=2(x+y)-4`
`or(y-x)^(2)=2(x+y-2)`
Vertex will be the point where the lines where the lines y-x=0 and x+y-2=0 meet, i.e., the point (1,1).