A treatise on plane co-ordinate geometryMacmillan & Company, 1855 |
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Side 86
... chord of contact . 100. Tangents are drawn to a circle from a given external point ; to find the equation to the chord of contact . Let h , k , be the co - ordinates of the external point ; x , y the co - ordinates of the point where ...
... chord of contact . 100. Tangents are drawn to a circle from a given external point ; to find the equation to the chord of contact . Let h , k , be the co - ordinates of the external point ; x , y the co - ordinates of the point where ...
Side 87
... chords are drawn to a circle , and tangents to the circle drawn at the extremities of each chord ; the locus of the intersection of the tangents is a straight line . Let h , k , be the co - ordinates of the point through which the chords ...
... chords are drawn to a circle , and tangents to the circle drawn at the extremities of each chord ; the locus of the intersection of the tangents is a straight line . Let h , k , be the co - ordinates of the point through which the chords ...
Side 87
... chord of III . If tangent a In the RR the от olar Equation . ir equation to the circle . P X X the initial line ; C the centre of the Es circumference . 1 , so that l , a , are the polar co - ordi- radius of the circle ; and let r , 0 ...
... chord of III . If tangent a In the RR the от olar Equation . ir equation to the circle . P X X the initial line ; C the centre of the Es circumference . 1 , so that l , a , are the polar co - ordi- radius of the circle ; and let r , 0 ...
Side 88
... chord of contact is Since ( x ' , y ' ) is on ( 1 ) xx ' + yy ' = c2 .... Ax ' + By + C = 0 ; therefore ( 2 ) may be written ( 2 ) . or , xx ' - y Ax ' + C B - B ( x - 4 ) x ' . Ay B = - c2 , c = 0 .... = 0 ........ ( 3 ) . Now ...
... chord of contact is Since ( x ' , y ' ) is on ( 1 ) xx ' + yy ' = c2 .... Ax ' + By + C = 0 ; therefore ( 2 ) may be written ( 2 ) . or , xx ' - y Ax ' + C B - B ( x - 4 ) x ' . Ay B = - c2 , c = 0 .... = 0 ........ ( 3 ) . Now ...
Side 89
... chord through ( h , k ) . ( Art . 101. ) II . If ( h , k ) be an external point , the equation represents the chord of contact . ( Art . 100. ) III . If ( h , k ) be on the circle , the equation represents the tangent at that point ...
... chord through ( h , k ) . ( Art . 101. ) II . If ( h , k ) be an external point , the equation represents the chord of contact . ( Art . 100. ) III . If ( h , k ) be on the circle , the equation represents the tangent at that point ...
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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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