Question

I WILL GIVE BRAINLIEST

Answer 1

 The correct option is: (B) x2=−4(y−1)

Explanation:

The distance between (x,y) and the focus point is: $\sqrt{(x-x_o)^2 + (y-y_o)^2}$ (Distance formula)

$x_o = 0 \\ y_o = 0$

Plug in the values; the expression becomes: $\sqrt{x^2 + y^2}$

The distance between (x,y) and the directrix y = 2: $\sqrt{(y-2)^2}$

In parabola both distances are equal; therefore

$\sqrt{x^2 + y^2}$ = $\sqrt{(y-2)^2}$

Take square on both sides:

$x^2 + y^2 = (y-2)^2 \\ x^2 + y^2 = y^2 + 4 - 4y \\ x^2 = 4-4y \\ x^2 = -4(y-1)$

Hence the correct option is: (B) x2=−4(y−1)