Analytic Geometry for Colleges, Universities, And Technical Schools
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(4) for the equation of the parabola when referred to O'Y', O'X', Fig. 33. The form of (4) shows that for every value assumed for x, y has two values, equal but of opposite sign ; hence, OX 9 bisects all chords, drawn parallel to OY' and is therefore a diameter of the parabola.
NOTE. A DIAMETER of a curve is a line which bisects a sys- tem of parallel chords.
71. To show that the parameter of any diameter is equal to four times the distance from the focus to the point in which that diameter cut...s the curve.
Draw the focal line FO' and the normal O'X, Fig. 33.
Since the triangle O'FT is isosceles, Art. 64, the angle O'FX = 2 XT COS MoreLess
To quickly assess the difficulty of the text, read a short excerpt:
(4) for the equation of the parabola when referred to O'Y', O'X', Fig. 33. The form of (4) shows that for every value assumed for x, y has two values, equal but of opposite sign ; hence, OX 9 bisects all chords, drawn parallel to OY' and is therefore a diameter of the parabola.
NOTE. A DIAMETER of a curve is a line which bisects a sys- tem of parallel chords.
71. To show that the parameter of any diameter is equal to four times the distance from the focus to the point in which that diameter cut...s the curve.
Draw the focal line FO' and the normal O'X, Fig. 33.
Since the triangle O'FT is isosceles, Art. 64, the angle O'FX = 2
= p ; sin
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