Find the equation of the ellipse with the given properties center (4,1) vertex (4,4) focus (4,3) What is the equation of the ellipse?

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Answer 1 · 2018-07-11T10:25:48

The equation is #(x-4)^2/5+(y-1)^2/9=1#

The general equation of an ellipse is

#(x-h)^2/b^2+(y-k)^2/a^2=1#

Here,

The center is #C=(h,k)=(4,1)#

One vertex is #V=(h,k+a)=(4,4)#

One focus is #F=(h,k+c)=(4,3)#

We can conclude that

#a=4-1=3#

#c=3-1=2#

#a^2=b^2+c^2#

Therefore,

#b^2=a^2-c^2=9-4=5#

The equation is

#(x-4)^2/5+(y-1)^2/9=1#

graph{((x-4)^2/5+(y-1)^2/9-1)=0 [-7.9, 7.9, -3.95, 3.95]}