A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and the Conic SectionsMacmillan, 1862 - 326 páginas |
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Página 92
... 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 ...
Página 93
... chord of con- tact is xh + yk = c2 ..... ( 4 ) . For ( 4 ) is obviously the equation to some straight line ; also this line passes through ( x , y ) , for ( 4 ) is satisfied by the values x = x , y = y , as we see ... CHORD OF CONTACT . 93.
... chord of con- tact is xh + yk = c2 ..... ( 4 ) . For ( 4 ) is obviously the equation to some straight line ; also this line passes through ( x , y ) , for ( 4 ) is satisfied by the values x = x , y = y , as we see ... CHORD OF CONTACT . 93.
Página 94
... contact will all pass through a fixed point . Let Ax + By + C = 0 .... ..... . ( 1 ) be the equation to the straight line ; let ( x ' , y ' ) be a point in this line from which tangents are drawn to the circle ; then ... CHORD OF CONTACT .
... contact will all pass through a fixed point . Let Ax + By + C = 0 .... ..... . ( 1 ) be the equation to the straight line ; let ( x ' , y ' ) be a point in this line from which tangents are drawn to the circle ; then ... CHORD OF CONTACT .
Página 95
... 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 ...
Página 108
... contact ; and the given point is the pole of the line . This definition might be misunderstood . For the equa- tion ... chord through the given point ; and the given point is called the pole of this straight line . If the given point be ...
... contact ; and the given point is the pole of the line . This definition might be misunderstood . For the equa- tion ... chord through the given point ; and the given point is called the pole of this straight line . If the given point be ...
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Términos y frases comunes
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
Pasajes populares
Página 100 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Página 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.
Página 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.
Página 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.
Página 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.