A treatise on plane co-ordinate geometryMacmillan & Company, 1855 |
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Side 104
... focus , and the fixed straight line the directrix . 124. It will be shewn hereafter that if a cone be cut by a plane , the curve of intersection will be one of the following ; a parabola , an ellipse , an hyperbola , a circle , two ...
... focus , and the fixed straight line the directrix . 124. It will be shewn hereafter that if a cone be cut by a plane , the curve of intersection will be one of the following ; a parabola , an ellipse , an hyperbola , a circle , two ...
Side 107
... focus of a conic section is called the Latus Rectum . Thus in the figure in Art . 126 , LSL ' is the Latus Rectum . Let xa , then from the equation y = 4ax , y = ± 2a . Hence LS L'S = 2a ; and LL ' = 4a . = 129. To express the focal ...
... focus of a conic section is called the Latus Rectum . Thus in the figure in Art . 126 , LSL ' is the Latus Rectum . Let xa , then from the equation y = 4ax , y = ± 2a . Hence LS L'S = 2a ; and LL ' = 4a . = 129. To express the focal ...
Side 112
... focus . Let x , y , be the co - ordinates of any point P on the curve ; the equation to the tangent at Pis 2a y = ( x + x ) y ' ( 1 ) . The equation to a line through the focus perpendicular to ( 1 ) is y ' y = - ( x − a ) 2a - ( 2 ) ...
... focus . Let x , y , be the co - ordinates of any point P on the curve ; the equation to the tangent at Pis 2a y = ( x + x ) y ' ( 1 ) . The equation to a line through the focus perpendicular to ( 1 ) is y ' y = - ( x − a ) 2a - ( 2 ) ...
Side 113
Isaac Todhunter. The point thus determined is the focus ; this however is not the locus of the intersection of ( 1 ) and ( 2 ) , for the values in ( 7 ) , although they satisfy ( 2 ) , do not satisfy ( 1 ) . We conclude therefore that ...
Isaac Todhunter. The point thus determined is the focus ; this however is not the locus of the intersection of ( 1 ) and ( 2 ) , for the values in ( 7 ) , although they satisfy ( 2 ) , do not satisfy ( 1 ) . We conclude therefore that ...
Side 114
... focus ; equation ( 1 ) remains as in Art . ( 138 ) ; instead of ( 2 ) we have , by Art . 45 , 2α + tan B ( x - a ) 2a 1 tan B У 2a + y'tan B = - ( x − a ) . y ' - 2a tan B Instead of ( 5 ) in Art . 138 , we shall find , y ' : = 2a ( x ...
... focus ; equation ( 1 ) remains as in Art . ( 138 ) ; instead of ( 2 ) we have , by Art . 45 , 2α + tan B ( x - a ) 2a 1 tan B У 2a + y'tan B = - ( x − a ) . y ' - 2a tan B Instead of ( 5 ) in Art . 138 , we shall find , y ' : = 2a ( x ...
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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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