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 170
... P ; then the equa- tion to CP is y = 2 х ( 1 ) . Since the conjugate diameter DD ' is parallel to the tangent at P , the equation to DD ' is b2x2 y x ..... a'y ( 2 ) . Y B B ' I We must combine ( 2 170 CONJUGATE DIAMETERS OF THE ELLIPSE .
... P ; then the equa- tion to CP is y = 2 х ( 1 ) . Since the conjugate diameter DD ' is parallel to the tangent at P , the equation to DD ' is b2x2 y x ..... a'y ( 2 ) . Y B B ' I We must combine ( 2 170 CONJUGATE DIAMETERS OF THE ELLIPSE .
Σελίδα 171
... conjugate diameters are numerous and important ; we shall now give a few of them . 193. The sum of the squares of two conjugate semi CONJUGATE DIAMETERS OF THE ELLIPSE . 171.
... conjugate diameters are numerous and important ; we shall now give a few of them . 193. The sum of the squares of two conjugate semi CONJUGATE DIAMETERS OF THE ELLIPSE . 171.
Σελίδα 172
... conjugate semi - diame- ters is equal to the sum of the squares of the semi - axes . Moreover 12 b2 CD2 = a2 + b2 — x'2 — y2 = a2 + b2 — x'2 — — 23 ( a2 — x12 ) b2 = a2 -- - - a2 — x22 = a2 — e2x22 ... CONJUGATE DIAMETERS OF THE ELLIPSE .
... conjugate semi - diame- ters is equal to the sum of the squares of the semi - axes . Moreover 12 b2 CD2 = a2 + b2 — x'2 — y2 = a2 + b2 — x'2 — — 23 ( a2 — x12 ) b2 = a2 -- - - a2 — x22 = a2 — e2x22 ... CONJUGATE DIAMETERS OF THE ELLIPSE .
Σελίδα 173
... conjugate semi- diameters ; a the angle between them ; by the preceding article .. sina : = a2b2 12 = a'b ' sin a = ab ; 4a2b2 4a2b2 a'2 b ' — ( a ” + b ′′ ) 2 — ( a'2 — b'2 ) 2 ̄ ̄ ( a2 + b2 ) 2 — ( a'2 — b'2 ) ” • Hence sina has its ...
... conjugate semi- diameters ; a the angle between them ; by the preceding article .. sina : = a2b2 12 = a'b ' sin a = ab ; 4a2b2 4a2b2 a'2 b ' — ( a ” + b ′′ ) 2 — ( a'2 — b'2 ) 2 ̄ ̄ ( a2 + b2 ) 2 — ( a'2 — b'2 ) ” • Hence sina has its ...
Σελίδα 174
... conjugate diameters as axes . = Let CP , CD be two conjugate semi - diameters ( see fig . to Art . 192 ) , take CP as the new axis of x , CD as that of y ; let PCA = a , DCA B. Let x , y be the co - ordinates of any point of the ellipse ...
... conjugate diameters as axes . = Let CP , CD be two conjugate semi - diameters ( see fig . to Art . 192 ) , take CP as the new axis of x , CD as that of y ; let PCA = a , DCA B. Let x , y be the co - ordinates of any point of the ellipse ...
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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.