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 8
... represents , we may give a geometrical definition of a curve and deduce from that definition an appropriate equation ; this will likewise appear as we proceed ; we shall take successively different curves , define them , deduce their ...
... represents , we may give a geometrical definition of a curve and deduce from that definition an appropriate equation ; this will likewise appear as we proceed ; we shall take successively different curves , define them , deduce their ...
Página 13
... represents a straight line . The general equation of the first degree with two variables is of the form Ax + By + C ... represents a straight line . If A = 0 , then by Art . 15 the line represented by ( 1 ) is parallel to the axis of x ...
... represents a straight line . The general equation of the first degree with two variables is of the form Ax + By + C ... represents a straight line . If A = 0 , then by Art . 15 the line represented by ( 1 ) is parallel to the axis of x ...
Página 14
... represents a line parallel to the axis of y . Hence the equation Ax + By + C = 0 always represents a straight line . 17. Equation in terms of the intercepts . The equation to a line may also be expressed in terms of its intercepts on ...
... represents a line parallel to the axis of y . Hence the equation Ax + By + C = 0 always represents a straight line . 17. Equation in terms of the intercepts . The equation to a line may also be expressed in terms of its intercepts on ...
Página 15
... represents ; therefore we need only determine one other point in it . Sup- pose x = 1 , then y = 1 ; here another ... represents a line passing through the origin and making with the axis of x an angle of which the tangent Hence y = x ...
... represents ; therefore we need only determine one other point in it . Sup- pose x = 1 , then y = 1 ; here another ... represents a line passing through the origin and making with the axis of x an angle of which the tangent Hence y = x ...
Página 16
Isaac Todhunter. Similarly the equation y = -x represents a line inclined to the axis of x at an angle of which the tangent is -1 ; that is , at an angle of 135 ° . Hence this equation represents a line through O bisecting the angle ...
Isaac Todhunter. Similarly the equation y = -x represents a line inclined to the axis of x at an angle of which the tangent is -1 ; that is , at an angle of 135 ° . Hence this equation represents a line through O bisecting the angle ...
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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.