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Question

The equation of a directrix of the ellipsex216+y225=1 is


A

3y=±5

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B

y=±5

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C

3y=±25

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D

y=±3

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Solution

The correct option is C

3y=±25


Explanation for the correct option:

The general equation of ellipse is x2b2+y2a2=1 , where a>b.

Given, x216+y225=1b=4,a=5

Step 1: Calculating the value of e,

e=1-b2a2=1-162252=35

Equation of directrix, y=±ae

Step 2 :Substituting the values of aande. To Calculate the value of y:

y=±5353y=±25

Hence, option (C) is the correct answer.


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