Question

Any point on the parabola whose focus is (0, 1) and the directrix is x+2=0 is given by

• A. $t^2+1,2t-1$
• B. $t^2+1,2t+1$
• C. $t^2,2t$
• D. $t^2-1,2t+1$

Answer 1

The correct option is D

$t^2-1,2t+1$

Any point on the parabola is equidistant from the focus and the directrix.
$\Rightarrow (x-0{)}^2+(y-1{)}^2={\left(\frac{x+2}{\sqrt{1}}\right)}^{2}or(y-1{)}^2=4(x+1)Clearly,x=t^2-1andy=2t+1satisfyitforallt$