Expert: Paul Klarreich - 4/29/2008

Question
which one of the following ellipses has its center at  the point C(2,1)

this is what ive tried to do ,can you tell me which is right  ,thanks a lot
a.4x²+9y²-16x-18y-11=0
b.9x²+4y²-36x-4y+4=0
c.16x²+25y²-36x+50y-164=0


Answer
Questioner:   stahn
Category:  Advanced Math
Private:  No
 
Subject:  analytical geometry
Question:  which one of the following ellipses has its center at  the point C(2,1)

this is what ive tried to do ,can you tell me which is right, thanks a lot
a.4x²+9y²-16x-18y-11=0
b.9x²+4y²-36x-4y+4=0
c.16x²+25y²-36x+50y-164=0
..............................
Hi, Stahn,

I think you left something out.  You said:  "this is what I've tried to do", but then you just copied the question.  What DID you try to do?

It should have been:

4x² + 9y² - 16x - 18y - 11 = 0

4x²  - 16x + 9y² - 18y   = 11  << rearrange.

4(x² - 4x     )  + 9(y² - 2y     )   = 11  << factor (leave blanks)

4(x² - 4x + 4)  + 9(y² - 2y  +   1)   = 11 + 4(4) + 9(1)  << complete square

4(x - 2)²  + 9(y - 1)²   = 11 + 4(4) + 9(1)  << factor

Now deduce center is (2,1).

Do the same for the others.