The locus of the mid points of the chords passing through a fixed point $( \alpha , \beta )$ of the hyperbola, $\dfrac { x ^ { 2 } } { a ^ { 2 } } - \dfrac { y ^ { 2 } } { b ^ { 2 } } = 1$ is
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a circle with centre $\left( \dfrac { \alpha } { 2 } , \dfrac { \beta } { 2 } \right)$
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an ellipse with centre $\left( \dfrac { \alpha } { 2 } , \dfrac { \beta } { 2 } \right)$
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a hyperbola with centre $\left( \dfrac { \alpha } { 2 } , \dfrac { \beta } { 2 } \right)$
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straight line through $\left( \dfrac { \alpha } { 2 } , \dfrac { \beta } { 2 } \right)$