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 \( (9,-6) \).
The locus of mid points of focal chords of curve \( C \), is
(a) \( y^{2}=(x-1) \)
(b) \( y^{2}=2(x-1) \)
(c) \( y^{2}=(x+1) \)
(d) \( x^{2}=2(y+1) \)
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