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Equation of the common tangent to the parabolas : y^2 = 4ax; x^2 = 4ay ...
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Show that the perpendiculars from the centre upon all chords, which join the ends of perpendicular diameters, are of constant length in an ellipse. ...
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Prove that the locus of the intersection of AP with the straight line through A' perpendicular to A'P is a straight line which is perpendicular to the major axis of an ellipse. ...