If one of the member of the orthogonal trajectory of \( y^{2}=k x \) where \( k \) is a paramete...

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If one of the member of the orthogonal trajectory of \( y^{2}=k x \) where \( k \) is a parameter, is a conic \( c \) which passes through the point \( (2,0) \), then identify the correct statement(s) about \( c \) .
(a) Eccentricity of \( c \) is \( \frac{1}{\sqrt{2}} \)
(b) Director circle of the conic \( c \) is \( x^{2}+y^{2}=12 \)
(c) Focal length of \( c \) is 4
(d) Latus rectum of the conic \( c \) is \( 2 \sqrt{2} \)
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