How do you write an equation of an ellipse in standard form given focus at (0,0) and vertices at (2, pi/2) and (8, 3pi/2)?

1 Answer

Answer:

#x^2/16+(y+3)^2/25=1#

Explanation:

The center of the ellipse can be solved by obtaining the average value of the vertices at #(2, pi/2)=(0, 2)#and #(8, (3pi)/2)=(0, -8)#

Center #(h, k)=(0, -3)#

there is a focus at (0, 0), vertex at (0, 2) and center at (0, -3) so that #c=3# and #a=5# by computation.

solve #b#:

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

#5^2=b^2+3^2#

#b^2=25-9#
#b^2=16#
and #b=4#

the equation of the ellipse with vertical major axis is:

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

#(x-0)^2/4^2+(y--3)^2/5^2=1#

#x^2/16+(y+3)^2/25=1#

see the graph

graph{x^2/16+(y+3)^2/25=1[-20, 20,-10,10]}

have a nice day! from the Philippines..