A Geometrical Treatise On Conic Sections With Numerous Examples for the Use of S

Cover A Geometrical Treatise On Conic Sections With Numerous Examples for the Use of S
A Geometrical Treatise On Conic Sections With Numerous Examples for the Use of S
William Henry Drew
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25. To two parabolas which have a common focus and axis two tangents are drawn at right angles ; the locus of their intersection is a straight line parallel to the directrices.
2G. If any three tangents be drawn to a parabola, the circle described about the triangle so formed will pass through the focus, and the perpendiculars from the angles on the opposite sides intersect in the directrix.
27. A parabola touches one side of a triangle in its middle point, and the other two sides produced. Pro
...ve that the per- pendiculars drawn from the angles of the triangle upon any tangent to the parabola are in harmonical progression.
28. Two equal parabolas have the same axis and vertex, but are turned in opposite directions ; chords of one parabola are tangents to the other. Show that the locus of the middle point of the chords is a parabola whose latus rectum is one- third of that of the given parabola.
29. Two equal parabolas have the same focus, and their axes are at right angles to each other, and a normal to one of them is perpendicular to a normal of the other ; prove that the locus of the intersection of such lines is a parabola.


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