A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and the Conic SectionsMacmillan, 1862 - 326 σελίδες |
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Σελίδα 201
... asymptote , which we shall consider hereafter ; see Art . 255 . The asymptote itself may then count as one of the two tan- gents from the point ( h , k ) . If h = 0 and k = 0 the point ( h , k ) is the origin ; in this case the two ...
... asymptote , which we shall consider hereafter ; see Art . 255 . The asymptote itself may then count as one of the two tan- gents from the point ( h , k ) . If h = 0 and k = 0 the point ( h , k ) is the origin ; in this case the two ...
Σελίδα 213
... Asymptotes . 255. The properties of the hyperbola hitherto given have been similar to those of the ellipse ; we have now to consider some properties peculiar to the hyperbola . M X Let the equation to the hyperbola be y2 TO CONJUGATE ...
... Asymptotes . 255. The properties of the hyperbola hitherto given have been similar to those of the ellipse ; we have now to consider some properties peculiar to the hyperbola . M X Let the equation to the hyperbola be y2 TO CONJUGATE ...
Σελίδα 214
... = α x + √√ ( x2 − a3 ) ̄ ̄x + √√ ( x2 — a3 ) * If then the line MPQ be supposed to move parallel to itself from A , the distance PQ continually diminishes , and by taking CM large enough we may make PQ as small as 214 ASYMPTOTES .
... = α x + √√ ( x2 − a3 ) ̄ ̄x + √√ ( x2 — a3 ) * If then the line MPQ be supposed to move parallel to itself from A , the distance PQ continually diminishes , and by taking CM large enough we may make PQ as small as 214 ASYMPTOTES .
Σελίδα 215
... asymptote of the curve . Similarly the line CL ' , which has for its equation bx y α is an asymptote . Thus the equation x2 y2 a2 b2 - - includes both asymptotes . We may take the following de- finition . DEF . An asymptote is a ...
... asymptote of the curve . Similarly the line CL ' , which has for its equation bx y α is an asymptote . Thus the equation x2 y2 a2 b2 - - includes both asymptotes . We may take the following de- finition . DEF . An asymptote is a ...
Σελίδα 216
... asymptotes . And from Art . 250 it appears that as conjugate diameters increase indefinitely they approach to coincidence with one of the asymptotes . 259. The line joining the ends of conjugate diameters is parallel to one asymptote ...
... asymptotes . And from Art . 250 it appears that as conjugate diameters increase indefinitely they approach to coincidence with one of the asymptotes . 259. The line joining the ends of conjugate diameters is parallel to one asymptote ...
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a²b² a²b³ a²y abscissa asymptotes ax² axes axis of x b²x² bisects centre chord of contact circle conic section conjugate diameters conjugate hyperbola constant Crown 8vo cy² denote directrix distance Edition ellipse equa equal Examples external point find the equation find the locus fixed point focal chord focus given lines given point Hence the equation inclined latus rectum Let the equation line drawn line joining lines meet lines which pass major axis meet the curve middle point negative normal ordinate origin parabola parallel perpendicular point h point of intersection polar co-ordinates polar equation pole positive preceding article proposition radical axis radius ratio rectangular required equation respectively right angles shew shewn sides Similarly student suppose tangent tion triangle vertex x₁ y₁
Δημοφιλή αποσπάσματα
Σελίδα 100 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Σελίδα 304 - Or, four terms are in harmonical proportion, when the first is to the fourth as the difference of the first and second is to the difference of the third and fourth.
Σελίδα 25 - In this equation n is the tangent of the angle which the line makes with the axis of abscissae, and B is the intercept on this axis from the origin.
Σελίδα 141 - Thus a parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line (see fig.
Σελίδα 189 - Hyperbola is the locus of a point which moves so that its distance from a fixed point, called the focus, bears a constant ratio, which is greater than unity, to its distance from a fixed straight line, called the directrix.