Question 877943: Analyze the Conic Section (center, vertices intercepts ...)
(4x^2)+(9y^2)-40x+64 = 0
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Analyze the Conic Section (center, vertices intercepts ...)
(4x^2)+(9y^2)-40x+64 = 0
4x^2-40x+9y^2=-64
complete the square
4(x^2-10x+25)+9y^2=-64+100
4(x-5)^2+9y^2=36
This is an equation of an ellipse with horizontal major axis
Its standard form of equation:  , a>b, (h,k)=coordinates of center
For given ellipse:
center: (5,0)
a^2=9
a=3
length of major axis=2a=6
vertices: (5±a,0)=(5±3,0)=(2,0) and(8,0)
b^2=4
b=2
length of minor axis=2b=4
x-intercept:
set y=0
(x-5)^2/9=1
(x-5)^2=9
x-5=±√9=±3
x=5±3
x-intercept=2, 8
..
y-intercept
set x=0
(-5)^2/9+y^2/4=1
y^2/4=1-25/9=-16/9
y^2=-64/9
y-intercept: none
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