A family of curves has the property that the segment of the tangent between the point of tangenc...

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A family of curves has the property that the segment of the tangent between the point of tangency and the \( x \)-axis is bisected at the point of intersection with \( y \)-axis. A member \( C \) of this family passes through the point \( (9,-6) \).
Which one of the following statement is correct?
(a) Focus of \( C \) is \( (4,0) \)
(b) Director circle of \( C \) is \( x+4=0 \)
(c) Length of latus-rectum of \( C \) is 4 .
(d) The equation of tangent at vertex of \( C \) is \( y=0 \)
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