A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and the Conic SectionsMacmillan, 1862 - 326 páginas |
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... ellipse , and hyperbola , have been separately considered before the discussion of the general equation of the second degree , from the belief that the subject is thus presented in its most accessible form to students in the early ...
... ellipse , and hyperbola , have been separately considered before the discussion of the general equation of the second degree , from the belief that the subject is thus presented in its most accessible form to students in the early ...
Página 112
... ellipse , an hyperbola , a circle , two straight lines , one straight line , or a point . Hence the term conic section is applied to the parabola , ellipse , and hyperbola — and may be extended to include the circle , two straight lines ...
... ellipse , an hyperbola , a circle , two straight lines , one straight line , or a point . Hence the term conic section is applied to the parabola , ellipse , and hyperbola — and may be extended to include the circle , two straight lines ...
Página 140
... the lines drawn from the vertex to the points of contact of the tangents from ( h , k ) are represented by the equation hy2 = = 2x ( ky ― 2ax ) . CHAPTER IX . THE ELLIPSE . 158. To find the 140 EXAMPLES ON THE PARABOLA .
... the lines drawn from the vertex to the points of contact of the tangents from ( h , k ) are represented by the equation hy2 = = 2x ( ky ― 2ax ) . CHAPTER IX . THE ELLIPSE . 158. To find the 140 EXAMPLES ON THE PARABOLA .
Página 141
Isaac Todhunter. CHAPTER IX . THE ELLIPSE . 158. To find the equation to the ellipse . The ellipse is the locus of a point which moves so that its distance from a fixed point bears a constant ratio to its dis- tance from a fixed straight ...
Isaac Todhunter. CHAPTER IX . THE ELLIPSE . 158. To find the equation to the ellipse . The ellipse is the locus of a point which moves so that its distance from a fixed point bears a constant ratio to its dis- tance from a fixed straight ...
Página 142
... ellipse with the assumed origin and axes . 159. To find where the ellipse meets the axis of x , we put y = 0 in the equation to the ellipse ; thus ( x − p ) 3 = e2x2 ; - - .. x − p = ± ex ; p • .. x = 1 Fe p 1 ; then A and A ' are ...
... ellipse with the assumed origin and axes . 159. To find where the ellipse meets the axis of x , we put y = 0 in the equation to the ellipse ; thus ( x − p ) 3 = e2x2 ; - - .. x − p = ± ex ; p • .. x = 1 Fe p 1 ; then A and A ' are ...
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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.