How do you find the standard form given vertices Foci (-3,0) and (3,0) and y intercepts (0,-4) and (0,4)?

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Answer 1 · 2018-01-20T12:04:06

Standard form of the ellipse is #x^2/25+y^2/16=1#

Focii are at # (-3,0 and 3,0)# So distance of focii from

centre is #c=3# , y intercepts are at #(0,-4) and (0,4) :.#

distance of vertices at minor axis from centre is #b=4#

Let distance of vertices at major axis from centre is #a#.

Relationship among #a, b, and c# is #c^2=a^2-b^2#

#:. 3^2= a^2-4^2 or a^2 =3^2+4^2=25 :. a=5 ; a > b#

Major axis length #= 2a =2*5=10# and minor axis length

# =2b= 2*4=8# . Hence standard form of the ellipse is

#x^2/a^2+y^2/b^2=1 or x^2/5^2+y^2/4^2=1# or

#x^2/25+y^2/16=1#

graph{x^2/25+y^2/16=1 [-14.24, 14.24, -7.12, 7.12]} [Ans]