A treatise on plane co-ordinate geometryMacmillan & Company, 1855 |
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Side 162
... P ; then the equation to CP is y ' y = x . ( 1 ) . Since the conjugate diameter DD ' is parallel to the tangent at P the equation to DD ' is b2x y X a2y ( 2 ) . A P ' B B ' D ' A X 162 CONJUGATE DIAMETERS OF THE ELLIPSE .
... P ; then the equation to CP is y ' y = x . ( 1 ) . Since the conjugate diameter DD ' is parallel to the tangent at P the equation to DD ' is b2x y X a2y ( 2 ) . A P ' B B ' D ' A X 162 CONJUGATE DIAMETERS OF THE ELLIPSE .
Side 163
... conjugate diameters are numerous and important ; we shall now give a few of them . 193. The sum of the squares of two conjugate semi 11-2 CONJUGATE DIAMETERS OF THE ELLIPSE . 163.
... conjugate diameters are numerous and important ; we shall now give a few of them . 193. The sum of the squares of two conjugate semi 11-2 CONJUGATE DIAMETERS OF THE ELLIPSE . 163.
Side 164
Isaac Todhunter. 193. The sum of the squares of two conjugate semi - diameters is constant . Let x ' , y ' , be the co - ordinates of P ; then by the preceding article + CP ? + CD = x + y + a2y2 , b2x2 ... CONJUGATE DIAMETERS OF THE ELLIPSE .
Isaac Todhunter. 193. The sum of the squares of two conjugate semi - diameters is constant . Let x ' , y ' , be the co - ordinates of P ; then by the preceding article + CP ? + CD = x + y + a2y2 , b2x2 ... CONJUGATE DIAMETERS OF THE ELLIPSE .
Side 165
... conjugate semi- diameters ; a the angle between them ; by the preceding article a2b2 .. sin a = = a'b ' sin a = ab ; 4a2b2 = 4a2b2 a2b - 2 ( a ^ 2 + b22 ) 2 — ( a ́2 — b′2 ) 2 ( a2 + b2 ) 2 — ( a ́2 — b′2 ) 2 · Hence sin2 a has its ...
... conjugate semi- diameters ; a the angle between them ; by the preceding article a2b2 .. sin a = = a'b ' sin a = ab ; 4a2b2 = 4a2b2 a2b - 2 ( a ^ 2 + b22 ) 2 — ( a ́2 — b′2 ) 2 ( a2 + b2 ) 2 — ( a ́2 — b′2 ) 2 · Hence sin2 a has its ...
Side 166
... 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 ...
... 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 ...
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a² sin² a²b² abscissa asymptotes ax² axes axis of x b2 a² b²x² centre chord of contact circle conic section conjugate diameters conjugate hyperbola constant cos² cy² denote directrix distance draw PM ellipse equa equal equation y² external point find the equation find the locus fixed point focal chord focus given point given straight line Hence the equation inclined latus rectum Let the equation line drawn line joining line which passes major axis meets the curve middle point negative ordinate origin of co-ordinates parabola perpendicular point h point of intersection polar co-ordinates polar equation positive preceding article radical axis radius ratio rectangular respectively right angles second degree shew shewn sides Similarly straight line passing suppose tangent tangents are drawn tion triangle vertex x₁ x²² y₁
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