Question

y = 1.
ariel remembers that for any point (x, y) on the parabola, the distance to the focus is the same as the distance to the directrix. she finds that the distance from (x, y) to the directrix is y - 1. which expression should she set this equal to?
√x² + (y - 2)² √x² + y² + 4 x + y - 2 x² + (y - 2)²

Explanation:

Step1: Find the distance from \((x,y)\) to the focus \((0,2)\)

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here \(x_1 = x,y_1 = y,x_2=0,y_2 = 2\). So the distance is \(\sqrt{(x - 0)^2+(y - 2)^2}=\sqrt{x^{2}+(y - 2)^{2}}\).

Step2: Recall the property of parabola

For a parabola, the distance from any point \((x,y)\) on the parabola to the focus is equal to the distance from \((x,y)\) to the directrix.

Answer:

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