Find the coordinates of any point on the parabola whose focus is (0, 1) and directrix is `x+2=0`

Options

A. `(t^(2)+1, 2t-1)`
B. `(t^(2)+1, 2t+1)`
C. `(t^(2), 2t)`
D. `(t^(2)-1, 2t+1)`

Answer

D

Explanation

The equation of the parabola is given by `sqrt((x-0)^(2)+(y-1)^(2))=|(x+2)/(sqrt1+0)|`
`rArr" "x^(2)+(y=1)^(2)=(x+2)^(2)`
`rArr" "(y-1)^(2)=4(x+1)`
The parametrix coordinates of the point of this parabola are given by
`x+1=t^(2)" and "y-1=2t" i.e. "(t^(2)-1, 2t+1)`