What is the y coordinate for the center of the given ellipse?

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Homework Help Overview

The discussion revolves around finding the y coordinate for the center of an ellipse defined by the equation 8x^2 + y^2 - 4y = 2.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants discuss rewriting the equation in the general form of an ellipse and question how to complete the square. There is mention of using differentiation as an alternative method to find the center coordinates.

Discussion Status

The discussion includes various approaches to determine the center of the ellipse, with some participants offering methods while others express uncertainty about the steps involved. A specific coordinate for the center has been suggested, but it is not universally accepted.

Contextual Notes

Participants are navigating the process of transforming the given equation, with some constraints related to their understanding of algebraic techniques such as completing the square and differentiation.

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Find the y coordinate for the center of the ellipse given by the equation 8x^2 + y^2 - 4y = 2
 
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Try to rewrite the equation in the general form of an ellipse.

A (x - x0)2 + B (y - y0)2 = 0,

where the center is at x0, y0
 
i don't know how. how do you write it?
 
Do you know how to "complete the square"?
 
There is an easier method if you know differentiation. Differentiate the equation wrt x treating y as a constant to get a value for x, and similarly for y by treating x as a constant. The values of x and y you get are the coordinates of the center.
 
the center is at (0,3)
 

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