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
... values corresponding to the different points we consider , and we may express the statement that the co - ordinates of P are a and b , thus ; for the point P , x = a and y = b . 4. The lines X'OX , Y'OY , being indefinitely produced ...
... values corresponding to the different points we consider , and we may express the statement that the co - ordinates of P are a and b , thus ; for the point P , x = a and y = b . 4. The lines X'OX , Y'OY , being indefinitely produced ...
Página 3
... values of the polar co - ordinates and r , since there is here no ambiguity corresponding to that arising from the four compartments of the figure in Art . 4. It is however found convenient to use a similar convention to that in Art . 4 ...
... values of the polar co - ordinates and r , since there is here no ambiguity corresponding to that arising from the four compartments of the figure in Art . 4. It is however found convenient to use a similar convention to that in Art . 4 ...
Página 5
... values in ( 3 ) and we have PQ2 = r2 + r ̧2 − 2r ̧r , cos ( 0 , — 01 ) . - 12 2 - " This result can also be obtained immediately from the tri- angle POQ formed by drawing lines from P and Q to the origin . 10 . To find the co ...
... values in ( 3 ) and we have PQ2 = r2 + r ̧2 − 2r ̧r , cos ( 0 , — 01 ) . - 12 2 - " This result can also be obtained immediately from the tri- angle POQ formed by drawing lines from P and Q to the origin . 10 . To find the co ...
Página 8
... value of y . Thus corresponding to the values 1 , 2 , 3 , ... of x , we have the values 3 , 4 , 5 , of Now suppose a line , straight or curved , such that it passes through every point determined by giving to x and y values that satisfy ...
... value of y . Thus corresponding to the values 1 , 2 , 3 , ... of x , we have the values 3 , 4 , 5 , of Now suppose a line , straight or curved , such that it passes through every point determined by giving to x and y values that satisfy ...
Página 10
... value of CD and AD in question 8 in terms of the co - ordinates there used ; and shew that AC2 + BC2 = 2 CD2 + 2AD2 . 12. Find the value of GA , GB , and GC , in question 9 in terms of the co - ordinates there used ; and shew that 3 ...
... value of CD and AD in question 8 in terms of the co - ordinates there used ; and shew that AC2 + BC2 = 2 CD2 + 2AD2 . 12. Find the value of GA , GB , and GC , in question 9 in terms of the co - ordinates there used ; and shew that 3 ...
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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.