Parabolic Equations Using Vertex & Focus

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The equation of the parabola with vertex (2, 4) and focus (2, 6) is derived using the formula (x-h)^2 = 4p(y-k), resulting in (x-2)^2 = 8(y-4). There is a discussion on whether to isolate a variable or leave the equation in its current form, with suggestions to group constants for clarity. Dividing through by 8 is mentioned as optional, depending on teacher preferences. The conversation emphasizes that similar to a circle's equation, isolation of variables is not always necessary. The focus remains on understanding the equation's structure rather than strict formatting.
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Homework Statement



Write the equation of the parabola described.
Vertex: (2, 4) Focus: (2,6)

Homework Equations



(x-h)^2 = 4p(y-k)


The Attempt at a Solution



(x-2)^2 = 4(2)(y-4)
x^2-4x+4 = 8y -32

Do I need to isolate one of the variables, or can I leave the equation like this?
 
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I'd at least group your constants, to make it look nicer. After you've done that, you could divide through by 8, but it isn't strictly required (unless your teacher said so). Afterall, an equation for a circle is x^2 + y^2 = 1, and that doesn't have an 'isolated' variable.
 

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