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Question

Find the equation of the directrix of the ellipse x2100+y236=1.

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Solution

Given the equation of the ellipse x2100+y236=1.

Now comparing this equation with x2a2+y2b2=1 we get, a=10,b=6.

Then eccentricity (e)=1b2a2=136100=64100=810.

Now equations of directrix are
x=±ae=±10810 or, 8x=±100 or, 2x=±25.

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