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Find the locus of the mid-points of the ...

Find the locus of the mid-points of the chords of the hyperbola `x^2-y^2=1` which touch the parabola `y^2 = 4x`.

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The locus of the mid-point of the chords of the hyperbola x^(2)-y^(2)=4 , that touches the parabola y^(2)=8x is

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Find the locus of the middle points of the chords of the parabola y^(2) = 4x which touch the parabola x^(2) = -8y .

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The locus of the middle points of the focal chords of the parabola, y^2=4x is:

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