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

Difficult

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)

Solution

The locus of focus lies on the circle with center $(\frac{3}{2}, 0)$ and radius $\frac{3}{2}$ , along the minor arc from $(2, \sqrt{2}) to (2, - \sqrt{2})$

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