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**Converting to Standard Form of an ellipse**

How do I convert to standard form so that I can graph an ellipse? What are the steps involved?

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**Review: What is standard form?**

Horizontal Ellipse OR Vertical Ellipse

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**Lets Do it! Graph the ellipse given by Step 1:**

Group x and y terms together and add 39 to both sides Step 2: Factor out the common factor, 4 is common factor to the x terms and 25 is common factor to the y terms Step 3: Complete the square of x and y. (b/2)². Multiply (b/2)² by the coefficients and add to the other side.

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**Continuation of example 1**

Step 4: Simplify; condense into perfect squares and add the right side Step 5: Divide by 100 to get the right side of your equation equal to 1. 25>4 , therefore the ellipse is horizontal a= b= (h,k) = (-3,1) Since a=5 , the vertices are 5 units to the left and right of the center, major axis vertices=(-8,1) and (2,1) Since b=2, the vertices are 2 units up and down from the center, minor axis vertices =(-3,-1) and (-3,3)

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Example 2 Convert to Standard Form and Graph

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Example 2

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