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Q.

An ellipse passes through (2, 0), (6, 0) and its directrix is the line y = x

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a

The locus of corresponding focus is a circle or a part of a circle

b

An insect moves tracing locus of corresponding focus, distance moved by the insect is d, then d lies in (3, 10)

c

The locus of corresponding focus is a Hyperbola

d

An insect moves tracing locus of corresponding focus, distance moved by the insect is d, then d lies in (10, 19)

answer is A.

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Detailed Solution

The locus of focus lies on the circle with center  32,0 and radius 32 , along the minor arc from (2,2) to (2,−2)
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An ellipse passes through (2, 0), (6, 0) and its directrix is the line y = x