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 86
... Normal to a Circle . 90. DEF . Let two points be taken on a curve and a secant drawn through them ; let the first point remain fixed and the second point move on the curve up to the first ; the secant in its limiting position is called ...
... Normal to a Circle . 90. DEF . Let two points be taken on a curve and a secant drawn through them ; let the first point remain fixed and the second point move on the curve up to the first ; the secant in its limiting position is called ...
Página 91
... normal at any point of a curve is a straight line drawn through that point perpendicular to the tangent to the curve at that point . 98. To find the equation to the normal at any point of a · circle . Let the equation to the circle be ...
... normal at any point of a curve is a straight line drawn through that point perpendicular to the tangent to the curve at that point . 98. To find the equation to the normal at any point of a · circle . Let the equation to the circle be ...
Página 92
... normal at any point passes through the origin of co - ordi- nates , that is , through the centre of the circle . 99. From any external point two tangents can be drawn to a circle . Let the equation to a circle be x2 + y2 = c3 ...
... normal at any point passes through the origin of co - ordi- nates , that is , through the centre of the circle . 99. From any external point two tangents can be drawn to a circle . Let the equation to a circle be x2 + y2 = c3 ...
Página 115
... normal to a Parabola . 130. To find the equation to the tangent at any point of a parabola . ( See Def . Art . 90. ) Let x ' , y ' be the co - ordinates of the point , x " , y " the co - ordinates of an adjacent point on the curve . The ...
... normal to a Parabola . 130. To find the equation to the tangent at any point of a parabola . ( See Def . Art . 90. ) Let x ' , y ' be the co - ordinates of the point , x " , y " the co - ordinates of an adjacent point on the curve . The ...
Página 118
... normal at ( x ' , y ' ) . ( 2 ) . 135. The equation to the normal may also be expressed in terms of the tangent of the angle which the line makes with the axis of the curve . For the equation to the normal is y Y2 x + y2 + Y'2x2 y ' y'x ...
... normal at ( x ' , y ' ) . ( 2 ) . 135. The equation to the normal may also be expressed in terms of the tangent of the angle which the line makes with the axis of the curve . For the equation to the normal is y Y2 x + y2 + Y'2x2 y ' y'x ...
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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.