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How do you find the foci and sketch the ellipse #1/4x^2+4y^2=1#?

1 Answer

Vinícius Ferraz

Mar 14, 2017

The ellipse passes through #(±2, 0)# and #(0, ±1/2)#.
It's laying #(a > b)# then the foci are on #x# axis, aren't they?

Explanation:

#x^2 / a^2 + y^2 / b^2 = 1 ; a = 2 ; b = 1/2#

When #y = 0#, #x^2 = 4 Rightarrow x = ± 2#

When #x = 0#, #4y^2 = 1 Rightarrow y = ± 1/2#

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

#c = sqrt{4 + 1/4} = sqrt 17 / 2#

I don't remember whether the foci are #(±c, 0)# or #(0, ±c)#

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