How do you write an equation of an ellipse for the given Foci (0,±8) Co-Vertices (±8,0)?

1 Answer
Leland Adriano Alejandro
Jan 29, 2016

#x^2/64+y^2/128=1#

Explanation:

From the given:
Foci: #F_1(0, 8), F_2(0, -8)#
Co-vertices at #(8, 0) # and (-8, 0)#

by inspection, the center of the ellipse is at Origin #(0, 0)#
that means

Center #(h, k)=(0, 0)#

Also, by inspection, #c=8# the distance from the center to a focus.
Also, #b=8# the distance from the center to one end point of the minor axis also called semi-minor axis length.

Compute for semi-major axis length #a#:

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

#a=sqrt(b^2+c^2)#

#a=sqrt(8^2+8^2)=sqrt(64+64#

#a=sqrt(2*64)#

#a=8sqrt(2)#

Use now the standard Form of the equation of ellipse for Vertical Major Axis.

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

Let us put on the values of #h=0, k=0, a=8sqrt(2), b=8#

#(x-0)^2/8^2+(y-0)^2/(8sqrt(2))^2=1#

#x^2/64+y^2/128=1#

Kindly check the graph ....
graph{(x^2/64+y^2/128-1)=0[-25,25,-15,15]}

Have a nice day !!! from the Philippines...

Related questions
See all questions in Standard Form of the Equation
Impact of this question
23210 views around the world
You can reuse this answer
Creative Commons License