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 1
... drawn at right angles . Let P be any other point in the plane ; draw PM parallel to OY meeting OX in M , and PN parallel to OX meeting OY in N. The position of P is evidently known if OM and ON are known ; for if through N and M lines be ...
... drawn at right angles . Let P be any other point in the plane ; draw PM parallel to OY meeting OX in M , and PN parallel to OX meeting OY in N. The position of P is evidently known if OM and ON are known ; for if through N and M lines be ...
Página 13
... drawn C meeting the axis of y at a distance from the origin - B and making with the axis of x an angle of which the tangent A is , then ( 2 ) will be the equation to this line . Hence ( 2 ) , B ' and therefore also ( 1 ) , represents a ...
... drawn C meeting the axis of y at a distance from the origin - B and making with the axis of x an angle of which the tangent A is , then ( 2 ) will be the equation to this line . Hence ( 2 ) , B ' and therefore also ( 1 ) , represents a ...
Página 15
... drawn . The line may also be constructed by comparing the given equation with the form in Art . 14 , y = mx . This we know represents a line passing through the origin and making with the axis of x an angle of which the tangent Hence y ...
... drawn . The line may also be constructed by comparing the given equation with the form in Art . 14 , y = mx . This we know represents a line passing through the origin and making with the axis of x an angle of which the tangent Hence y ...
Página 29
... drawn parallel to a given straight line . 39. To determine the co - ordinates of the point of intersec- tion of two given straight lines . Let the equation to one line be y = m12 x + c1 ....... .. ( 1 ) , and the equation to the other y ...
... drawn parallel to a given straight line . 39. To determine the co - ordinates of the point of intersec- tion of two given straight lines . Let the equation to one line be y = m12 x + c1 ....... .. ( 1 ) , and the equation to the other y ...
Página 35
... sion of the subject by applying the general formulæ to special examples . He will find it useful to illustrate these cases by figures . 47. To find the length of the perpendicular drawn from 3-2 EQUATIONS TO CERTAIN LINES . 35.
... sion of the subject by applying the general formulæ to special examples . He will find it useful to illustrate these cases by figures . 47. To find the length of the perpendicular drawn from 3-2 EQUATIONS TO CERTAIN LINES . 35.
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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.