...hyperbola has the same focus and directrix as the parabola, and that its eccentricity = sec0. Ex. 8. Find the locus of the foot of the perpendicular from the focus of a parabola on the normal. The length of the perpendicular from (m, 0) on 2m (y - y') + y (x — x") =...

...— cos' a", &c. Therefore adding the two preceding equations, we have for the equation of the locus, a cone concyclic with the reciprocal of the given...the reciprocal of the given cone. 226. To find the loeus of the foot of the perpendicular from the focus of a sphero-conic on the tangent. The work of...

...preceding equations, we have for the equation of the locus, Ax' + J5/ + Cz> = (A + B+ C] (of +/ + **), a cone concyclic with the reciprocal of the given...with the reciprocal of the given cone. 226. To find ike locus of the foot of the perpendicular from the focus of a sphero-conic on the tangent. The work...

...normal bisects the angle between the focal distances. The tangent bisects the supplemental angle. 127. To find the locus of the foot of the perpendicular from the focus on the tangent. If y-mx = ija*m* + 1>* ..................... (1) be any tangent, the perpendicular...

...a) y2 = 0. These two lines cut at right angles (Art. 74) it 2p2 + 2p (g cosa +/sina) + c = 0. Ex. 6. To find the locus of the foot of the perpendicular from the origin on a chord which subtends a right angle at the origin. The polar co-ordinatea of the locus arep...

...ellipse. 1 1. Given two normals to a parabola and the axis, determine the focus and directrix. 12. Find the locus of the foot of the perpendicular from the focus of an ellipse on a chord subtending a constant angle at the focus. Classi<s. HERODOTUS. Mit. GRAY. Translate...

...TRAILJ.. 6 Given two conjugate diameters of an ellipse in magnitude and position, find the axes. 7. Find the locus of the foot of the perpendicular from the focus of a parabola on any normal. 8. If ooz4 + 481Xs + 6iz.ia:* + 4as3; + a4 = o, find the transformed equation...

...Consequently TP, having one point on the curve and every other point outside the curve, is a tangent. 112. To find the locus of the foot of the perpendicular from the focus on the tangent. 113. The product of the perpendiculars from the foci on the tangent is equal to ft...

...equation to a conic section, the focns being the pole, and the equation to the tangent to it at any point. Find the locus of the. foot of the perpendicular from the focus on the tangent. 14. Prove that the locus of a point the sum of whose distances from two given points...

...(A + B+0} (at + y* + s"), a cone concyclic with the reciprocal of the given cone. ReciGG procally, the envelope of a chord 90° in length is a spheroconic, confocal with the reciprocal of the given cone. 254. To find tJie focus of the foot of the perpendicular from the focus of a sphero-conic on the tangent....