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 2
... figure in Art . 1 we have taken the angle YOX a right angle ; the axes are then called rectangular . If the angle YOX be not a right angle , the axes are called oblique . All that has been hitherto said applies whether the axes are ...
... figure in Art . 1 we have taken the angle YOX a right angle ; the axes are then called rectangular . If the angle YOX be not a right angle , the axes are called oblique . All that has been hitherto said applies whether the axes are ...
Página 3
... figure in Art . 4. It is however found convenient to use a similar convention to that in Art . 4 ; angles measured in one direction from OX are con- sidered positive and in the other negative . Thus if in the figure XOP be a positive ...
... figure in Art . 4. It is however found convenient to use a similar convention to that in Art . 4 ; angles measured in one direction from OX are con- sidered positive and in the other negative . Thus if in the figure XOP be a positive ...
Página 4
... figure , we may deduce x2 + y2 = r2 , y = = tan 0 . x 9. We proceed to investigate expressions for some geome- trical quantities in terms of co - ordinates . To find an expression for the length of the line joining two points . P R X ...
... figure , we may deduce x2 + y2 = r2 , y = = tan 0 . x 9. We proceed to investigate expressions for some geome- trical quantities in terms of co - ordinates . To find an expression for the length of the line joining two points . P R X ...
Página 5
... figures placing P and Q in the different compartments and in different positions ; the equa- tions ( 1 ) and ( 2 ) will be found universally true . From the equation ( 2 ) we have 2 2 PQ = x2 + y2 + x + y , − 2 ( x , x , + Y1Y1 ) ...
... figures placing P and Q in the different compartments and in different positions ; the equa- tions ( 1 ) and ( 2 ) will be found universally true . From the equation ( 2 ) we have 2 2 PQ = x2 + y2 + x + y , − 2 ( x , x , + Y1Y1 ) ...
Página 6
... figure that LN = AD AC = NM DR CB x that is , - X1 x2 - x = Similarly , n1x2 + n2x1 ..x = n1 + n2 192 y = n1 + n z In this article the axes may be oblique or rectangular . A simple case is that in which we require the co - ordinates of ...
... figure that LN = AD AC = NM DR CB x that is , - X1 x2 - x = Similarly , n1x2 + n2x1 ..x = n1 + n2 192 y = n1 + n z In this article the axes may be oblique or rectangular . A simple case is that in which we require the co - ordinates of ...
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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.