Q. 64.3( 3 Votes )

# The eccentricity of the ellipse, if the minor axis is equal to the distance between the foci is

A.

B.

C.

D.

Answer :

Given that we need to find the eccentricity of the ellipse whose minor axis is equal to the distance between the foci.

We know that distance between foci is 2ae and length of minor axis is 2b.

⇒ 2ae = 2b

⇒ b = ae

⇒ b^{2} = a^{2}e^{2}

We know that b^{2} = a^{2}(1 - e^{2})

⇒ a^{2}(1 - e^{2}) = a^{2}e^{2}

⇒ a^{2} = 2a^{2}e^{2}

⇒

⇒

∴ The correct option is C

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