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
... negative ; lines measured along Or are considered positive , and along OY ' negative . ( See Trigonometry , Chap . IV . ) If then we pro- duce PN to a point Q such that NQNP , we have for the point Q , xa , y = b . If we produce PM to R ...
... negative ; lines measured along Or are considered positive , and along OY ' negative . ( See Trigonometry , Chap . IV . ) If then we pro- duce PN to a point Q such that NQNP , we have for the point Q , xa , y = b . If we produce PM to R ...
Página 3
... negative . Thus if in the figure XOP be a positive angle , XOQ will be a negative angle ; if the angle XOQ be a quarter of a right angle , we may say that for XOQ , 0 = - . It is , as we have stated , not absolutely necessary to ...
... negative . Thus if in the figure XOP be a positive angle , XOQ will be a negative angle ; if the angle XOQ be a quarter of a right angle , we may say that for XOQ , 0 = - . It is , as we have stated , not absolutely necessary to ...
Página 4
... negative quantity , we measure it on the same line as if it had been a positive quantity but in the opposite direction from 0 . Hence if ẞ represent any angle and c any length the same point is determined by the polar co - ordinates B ...
... negative quantity , we measure it on the same line as if it had been a positive quantity but in the opposite direction from 0 . Hence if ẞ represent any angle and c any length the same point is determined by the polar co - ordinates B ...
Página 8
... negative . Locus of an equation . Equation to a curve . ... y . 12. Suppose an equation to be given between two unknown quantities , for example , y - x - 2 = 0 . We see that this equation has an indefinite number of solutions , for we ...
... negative . Locus of an equation . Equation to a curve . ... y . 12. Suppose an equation to be given between two unknown quantities , for example , y - x - 2 = 0 . We see that this equation has an indefinite number of solutions , for we ...
Página 11
... + QM = OB + QM = c + OM tan QOM = c + mx . Hence the required equation is y = mx + c . OB is called the intercept on the axis of y ; if the line crosses the axis of y on the negative side of ( 11 ) On the Straight Line.
... + QM = OB + QM = c + OM tan QOM = c + mx . Hence the required equation is y = mx + c . OB is called the intercept on the axis of y ; if the line crosses the axis of y on the negative side of ( 11 ) On the Straight Line.
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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.