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Question 596707: Write the equation of the ellipse 4x^2 + 9y^2 – 16x – 126y + 421 = 0 in standard form. I need help, please!
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! I have an entire section explaining this topic. Please see my website, which I will describe later. Meanwhile, here is your solution:
4x^2 + 9y^2 - 16x - 126y + 421 = 0
Collect the x and y terms together and leave a space to allow completing the square.
4x^2 - 16x + _____ + 9y^2 - 126y + _____ = -421
Factor out the coefficients of the "square" terms:
4(x^2 - 4x + ____) + 9(y^2 - 14y + _____) = -421 + _____ + _____
Now, for the x and y terms, take HALF and SQUARE and add to each side of the equation:
4(x^2 - 4x + 4) + 9(y^2 - 14y + 49) = -421 + 4*4 + 9*49
4(x-2)^2 + 9(y-7)^2 = -421+16+441
4(x-2)^2 + 9(y-7)^2 = 36
Divide both sides by 36 to set equal to 1:
This is standard form.
For additional explanation on ELLIPSES AND HYPERBOLAS, please see my own website. The easiest way to find it is to use the easy to spell and easy to remember link www.mathinlivingcolor.com. On this single page website, there is a link at the bottom of the page that takes you to my Homepage.
Near the top of my homepage, look for the link "Basic, Intermediate, and College Algebra: One Step at a Time", and choose College Algebra (Chapter 2), Section 2.05. There you will find explanations that may be easier to understand than your traditional textbooks, with lots of examples already solved for you. For problems like the one you posted here on algebra.com, look towards the end of the section. I have quite a few examples solved in detail and other exercises just like this one, that you may find helpful.
If you like my website, please tell your friends and family. It's all FREE. You can contact me by Email at rapaljer@seminolestate.edu.
Dr. Robert J. Rapalje, Retired
Professor of Mathematics
Seminole State College of Florida
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