Question

A parabola has its vertex at (2, 2), and the equation of its directrix is y = 2.5. The equation that represents the parabola is .

Answer 1

c) x^2 - 4x + 2y = 0

Explanation:

For plato this is the correct answer

Answer 2

check the picture below, based that the directrix is a horizontal line, and the vertex is below it, we know is a vertical parabola, and is opening downwards.

notice the distance "p" from the vertex to the directrix, is just 1/2


`\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} (y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\ \boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}})} \\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\`


`\bf (x-{{ h}})^2=4{{ p}}(y-{{ k}})\qquad \begin{cases} h=2\\ k=2\\ p=(1)/(2) \end{cases}\implies (x-2)^2=4\left( (1)/(2) \right)(y-2) \\\\\\ (x-2)^2=2(y-2)\implies \cfrac{1}{2}(x-2)^2=y-2\implies \boxed{\cfrac{1}{2}(x-2)^2+2=y}`