SOLUTION: 5. Identify the curve and sketch its graph. 25x^2 + 16y^2 +100x -32y � 284 = 0 (Hint: complete the square in both x and y if necessary)

Question 129115: 5. Identify the curve and sketch its graph.

25x^2 + 16y^2 +100x -32y � 284 = 0
(Hint: complete the square in both x and y if necessary)
Label important features of this graph.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Rearrange the terms

Add to both sides

Complete the square for the x terms

Complete the square for the y terms

Combine like terms

Add to both sides

Combine like terms

-----------

Now divide both sides by 400 to make the right side equal to 1

Simplify and break up the fraction

Reduce

So now the equation is in the form

which is the general equation of an ellipse. Where "a" is the horizontal diameter,"b" is the vertical diameter, and (h,k) is the center.

So in our case the horizontal diameter is , the vertical diameter is , and the center is (-2,1)

So if we graph , we get

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