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 12
... tangent of the 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 ...
... tangent of the 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 ...
Página 86
... Tangent and Normal to a Circle . 90. DEF . Let two points be taken on a curve and a secant drawn through them ; let ... tangent to the curve at the first point . 91. To find the equation to the tangent at any point of a circle . Let the ...
... Tangent and Normal to a Circle . 90. DEF . Let two points be taken on a curve and a secant drawn through them ; let ... tangent to the curve at the first point . 91. To find the equation to the tangent at any point of a circle . Let the ...
Página 87
... tangent at the point ( x ' , y ' ) is y - y ' : = - ( x - x ' ) .. y . ( 4 ) . This equation may be simplified ; by ... tangent can be conveniently ex- pressed in terms of the tangent of the angle which the line makes with the axis of x ...
... tangent at the point ( x ' , y ' ) is y - y ' : = - ( x - x ' ) .. y . ( 4 ) . This equation may be simplified ; by ... tangent can be conveniently ex- pressed in terms of the tangent of the angle which the line makes with the axis of x ...
Página 88
... tangent may be written y = mx + c √√ ( 1 + m2 ) . Conversely every line whose equation is of this form is a tangent to the circle . 93. The definition in Art . 90 may appear arbitrary to the student , and he may ask why we do not ...
... tangent may be written y = mx + c √√ ( 1 + m2 ) . Conversely every line whose equation is of this form is a tangent to the circle . 93. The definition in Art . 90 may appear arbitrary to the student , and he may ask why we do not ...
Página 89
... tangent to the circle . For suppose x2 + y2 = c2 to be the equation to a circle and y = mx + n the equation to a straight line ; to find the points of inter- section of the line and circle we combine the equations ; thus we obtain or ...
... tangent to the circle . For suppose x2 + y2 = c2 to be the equation to a circle and y = mx + n the equation to a straight line ; to find the points of inter- section of the line and circle we combine the equations ; thus we obtain or ...
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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.