A treatise on plane co-ordinate geometryMacmillan & Company, 1855 |
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Side 180
... to the normal at any point . 51. From any point P perpendiculars PM , PN , are drawn on the equal conjugate diameters ; shew that the normal at P bisects MN . CHAPTER XI . THE HYPERBOLA . 209. To find the 180 EXAMPLES ON THE ELLIPSE .
... to the normal at any point . 51. From any point P perpendiculars PM , PN , are drawn on the equal conjugate diameters ; shew that the normal at P bisects MN . CHAPTER XI . THE HYPERBOLA . 209. To find the 180 EXAMPLES ON THE ELLIPSE .
Side 181
Isaac Todhunter. CHAPTER XI . THE HYPERBOLA . 209. To find the equation to the hyperbola . The hyperbola is the locus of a point which moves so that its distance from a fixed point bears a constant ratio to its distance from a fixed ...
Isaac Todhunter. CHAPTER XI . THE HYPERBOLA . 209. To find the equation to the hyperbola . The hyperbola is the locus of a point which moves so that its distance from a fixed point bears a constant ratio to its distance from a fixed ...
Side 182
... hyperbola with the assumed origin and axes . 210. To find where the hyperbola meets the axis of x we put y = 0 in the equation to the hyperbola ; thus ( x − p ) 2 = e2x2 ; .. x − p = ± ex ; .. x = P 17 e Since e is greater than unity ...
... hyperbola with the assumed origin and axes . 210. To find where the hyperbola meets the axis of x we put y = 0 in the equation to the hyperbola ; thus ( x − p ) 2 = e2x2 ; .. x − p = ± ex ; .. x = P 17 e Since e is greater than unity ...
Side 183
... useful hereafter . Thus ( 1 ) may be written b2 y2 = ( 2αx + x2 ) .... ( 3 ) , and ( 2 ) may be written 32 b2 ' = = = = ( x2 - a2 ) .. a2 ( 4 ) , or , more symmetrically , x2 2-1 / 2 = EQUATION TO THE HYPERBOLA . 183.
... useful hereafter . Thus ( 1 ) may be written b2 y2 = ( 2αx + x2 ) .... ( 3 ) , and ( 2 ) may be written 32 b2 ' = = = = ( x2 - a2 ) .. a2 ( 4 ) , or , more symmetrically , x2 2-1 / 2 = EQUATION TO THE HYPERBOLA . 183.
Side 184
... hyperbola . Take the equation referred to the centre as origin , b2 y2 = = = ( x2 — a2 ) a2 - . ( 1 ) . For every value of x less than a , y is impossible . When x = a , y = 0 . For every value of x greater than a there S P K P Α ' AMH ...
... hyperbola . Take the equation referred to the centre as origin , b2 y2 = = = ( x2 — a2 ) a2 - . ( 1 ) . For every value of x less than a , y is impossible . When x = a , y = 0 . For every value of x greater than a there S P K P Α ' AMH ...
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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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