A Course of Pure Geometry Containing a Complete Geometrical Treatment of the Pr

Cover A Course of Pure Geometry Containing a Complete Geometrical Treatment of the Pr
A Course of Pure Geometry Containing a Complete Geometrical Treatment of the Pr
E H Edward Harrison Askwith
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QV':RU^-=PV:PU: THE PARABOLA 137 FV PU SP = 4SP. . -. QV"- = ^SP. PV.
(§ 133) It will be seen that the property FN- = 4 AS. AS of § 121 is only a special case of the general proposition just proved.
135. The preceding proposition shews that a parabola may be regarded as the locus of a point in a plane such that the square of its distance from a fixed line I varies as its distance from another fixed line I' not necessarily at right angles to /. The line I is a diameter of the parabola and I' is
...a tangent at the point where / and I' intersect.
If a be the angle which QV makes with the axis in § 134 QF=perp. From*Q on PF x cosec a.
and PF= perp. From Q on tangent at P x cosec a; . *. (Perp. From Q on PV)- x cosec- a = 4

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