SOLUTION: hello again i have another problem this time, i have a question on "elipse" and here is the problem =========== =========== =========== =========== ========== 4x^2+9y^2-16x-

Question 144041: hello again
i have another problem
this time, i have a question on "elipse"
and here is the problem
==========================================================
4x^2+9y^2-16x-18y=11
this is the expanded equation, so how do i find the STANDARD form of
this equation?? and how do i find the coordinates of 4 VERTICES???
including major and minor axis???
=============================================================
please tell me all the steps and i would appreciate it very MUCH!!!!!
thank you so much again
i have a quiz and i go this problem wrong
please tell me soon as possible
and have a great day ! THANK YOU!
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
4x^2+9y^2-16x-18y=11
this is the expanded equation, so how do i find the STANDARD form of
this equation?? and how do i find the coordinates of 4 VERTICES???
including major and minor axis???
-------------------------
1st: complete the square separately on the x and on the y terms to get:
[4x^2-16x] +[9y^2-18y] = 11
[4(x^2-4x+4)] + [9[y^2-2y+1)] = 11+4*4 + 9*1 = 36
Divide thru by 36 to get:
(x-2)^2/9 + (y-1)^2/4 = 1
This is the standard form of an ellipse:
-------------------------------
Center: (h,k) = (2,1)
-------------------------------
Semi-major axis = sqrt9 = 3
Semi-minor axis = sqrt4 = 2
------------------------------
Vertices on the major axis: (2+3,1) and (2-3,1)
vertices on the minor axis: (2,1+2) and (2,1-2)
---------------------------------
Cheers,
Stan H.

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