How do you graph #\frac { ( x - 3) ^ { 2} } { 9} + \frac { ( y - 5) ^ { 2} } { 25} = 1#?

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Answer 1 · 2018-08-07T14:19:11

See the explanation below.

This is the equation of an ellipse with a vertical major axis

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

Here, the equation is

#(x-3)^2/3^2+(y-5)^2/5^2=1#

#a=5#

#b=3#

#c=sqrt(a^2-b^2)=sqrt(25-9)=+-4#

The center of the ellipse is #C=(h,k)=(3,5)#

The vertices are

#A=(h.k+a)=(3,10)# and #A'=(h, k-a)=(3,0)#

And

#B=(h+b,k)=(6,5)# and #B'=(h-b,k)=(0,5)#

With the vertices, you can graph the ellipse.

graph{((x-3)^2/3^2+(y-5)^2/5^2-1)=0 [-8.84, 19.64, -0.63, 13.61]}