. Algebraic geometry; a new treatise on analytical conic sections . FlQ. 105. Draw any chord at rt. z. to VV and bisect it at N. Draw thediameter AN meeting the curve at A. AN is a diameter bisectinga chord at right angles; .. AN is the axis. Let VV meet the curve at P, and at P draw PT parallel to thechords through V and V to meet the axis at T. PT is the tangentat P. At P make the l TPS = L PTN, and let PS meet the axis at = ST;.. since PT is a tangent, S is the focus. Produce SA to X and make AX = AS. Draw KX at rt. C to is the directrix. ART. 174.] PROPERTIES OF THE PARABOLA
. Algebraic geometry; a new treatise on analytical conic sections . FlQ. 105. Draw any chord at rt. z. to VV and bisect it at N. Draw thediameter AN meeting the curve at A. AN is a diameter bisectinga chord at right angles; .. AN is the axis. Let VV meet the curve at P, and at P draw PT parallel to thechords through V and V to meet the axis at T. PT is the tangentat P. At P make the l TPS = L PTN, and let PS meet the axis at = ST;.. since PT is a tangent, S is the focus. Produce SA to X and make AX = AS. Draw KX at rt. C to is the directrix. ART. 174.] PROPERTIES OF THE PARABOLA. 155 173. To find the value of y-^ ^ iax-^ in connection mth the parabolaf = \.ax, when {^y, y.^, is not on the cuirve. Let P be the point (Kj, y-^,and draw PN perpendicular tothe axis to meet the curve in Qand Q. y.^ » 4aa;i = PN^ » 4a. AN = PN2 » QN^ = (PN+QN)(PN«QN) = ,for QQ is bisected at
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