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anonymous
 one year ago
Find the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = 2.
anonymous
 one year ago
Find the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = 2.

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Hero
 one year ago
Best ResponseYou've already chosen the best response.2@Nairz, what are your thoughts regarding this problem? Do you have an approach for solving this?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Im assuming the vertex is the origin since the directrix and the focus are both 2 units away from the origin along the same line.

Hero
 one year ago
Best ResponseYou've already chosen the best response.2Consider this: If you have two points, the focus \((x_1, y_1)\) and the directrix \((x_2, y_2)\) then you can insert those points in to the following formula to find the standard form of the equation of a parabola: \((x  x_1)^2 + (y  y_1)^2 = (x  x_2)^2 + (y  y_2)^2\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And that will give me the equation to the parabola?

Hero
 one year ago
Best ResponseYou've already chosen the best response.2Yes. Notice that in this case: Focus: \((x_1, y_1) = (0,2)\) Directrix: \((x_2, y_2) = (x,2)\)

Hero
 one year ago
Best ResponseYou've already chosen the best response.2You'll have to do a bit of simplification after inserting the points in order to express the equation in standard form.

Hero
 one year ago
Best ResponseYou've already chosen the best response.2@Nairz, mind showing your work for this? Let's see what equation you come up with.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ummm I got \[x=2\sqrt{2}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ill show my work in a second

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\large (x0)^2 + (y+2)^2 = (xx)^2 + (y2)^2\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\large x^2 + (y+2)^2 = (y+2)^2\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\large x^2 = (y2)^2  (y+2)^2\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\large x=2\sqrt{2}\]

Hero
 one year ago
Best ResponseYou've already chosen the best response.2\((y  2)^2  (y + 2)^2\) is actually "difference of squares". You should use the difference of squares formula to simplify that properly.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i dont have a formula sheet in front of me

Hero
 one year ago
Best ResponseYou've already chosen the best response.2Difference of squares formula: \(a^2  b^2 = (a + b)(a  b)\)

Hero
 one year ago
Best ResponseYou've already chosen the best response.2In this case a = y  2 b = y + 2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so its \[\large ((y2)+ (y+2))((y2)(y+2))\]

Hero
 one year ago
Best ResponseYou've already chosen the best response.2Don't forget the \(x^2\) equals part

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0simplified: \[\large x^2 = 2y(4)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0which isnt an option...

Hero
 one year ago
Best ResponseYou've already chosen the best response.2Note that the equation can also be written in the form \(y = \dfrac{1}{8}x^2\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok... I just realized I was looking at the wrong problem's answers... That is there. Thanks

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Can you work through another one of these with me? Just to make sure I do it correctly?
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