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
... 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 rectangular or oblique . We shall always ...
... 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 rectangular or oblique . We shall always ...
Página 3
... 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 angle , XOQ will be a negative angle ; if the angle XOQ be a quarter of a right angle , we may say ...
... 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 angle , XOQ will be a negative angle ; if the angle XOQ be a quarter of a right angle , we may say ...
Página 10
... angle AOB ; if C be the point where this line meets AB shew that the polar co - ordinates 2rr , cos ( 0,0 ) of Care 0 = ( 0 , + 02 ) and r = 12 11. Find the value of CD and AD in question 8 in terms of the co - ordinates there used ...
... angle AOB ; if C be the point where this line meets AB shew that the polar co - ordinates 2rr , cos ( 0,0 ) of Care 0 = ( 0 , + 02 ) and r = 12 11. Find the value of CD and AD in question 8 in terms of the co - ordinates there used ...
Página 12
... angle QOM or BAO , that is , the tangent of the angle which that part of the line which is above the axis of x makes with the axis of x pro- duced in the positive direction . Hence if the line through the origin parallel to the given ...
... angle QOM or BAO , that is , the tangent of the angle which that part of the line which is above the axis of x makes with the axis of x pro- duced in the positive direction . Hence if the line through the origin parallel to the given ...
Página 13
... 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 straight line . If A = 0 , then by Art . 15 the line represented by ( 1 ) is parallel to the axis ...
... 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 straight line . If A = 0 , then by Art . 15 the line represented by ( 1 ) is parallel to the axis ...
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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.