A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and the Conic SectionsMacmillan, 1862 - 326 σελίδες |
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Σελίδα 2
... the contrary be stated ; this remark applies both to our investigations and to the examples which are given for the exercise of the student . 6. Another method of determining the position of a point 2 CO - ORDINATES OF A POINT .
... the contrary be stated ; this remark applies both to our investigations and to the examples which are given for the exercise of the student . 6. Another method of determining the position of a point 2 CO - ORDINATES OF A POINT .
Σελίδα 3
... determined if we know the angle XOP and the distance OP . The angle is usually denoted by and the distance by r . 0 O is called the pole , OX the initial line ; OP the radius vector of the point P , and POX the vectorial angle . 7. The ...
... determined if we know the angle XOP and the distance OP . The angle is usually denoted by and the distance by r . 0 O is called the pole , OX the initial line ; OP the radius vector of the point P , and POX the vectorial angle . 7. The ...
Σελίδα 4
... determined by saying its = π co - ordinates are and a . Thus when the radius vector is a 4 -- negative quantity , we measure it on the same line as if it had been a positive quantity but in the opposite direction from 0 . Hence if ẞ ...
... determined by saying its = π co - ordinates are and a . Thus when the radius vector is a 4 -- negative quantity , we measure it on the same line as if it had been a positive quantity but in the opposite direction from 0 . Hence if ẞ ...
Σελίδα 5
... determined . If the axes are rectangular , we have PQ3 = ( x , − x ̧ ) 2 + ( Y2 — Y2 ) 2 .. - - .. ( 1 ) , ( 2 ) . The student should draw figures placing P and Q in the different compartments and in different positions ; the equa ...
... determined . If the axes are rectangular , we have PQ3 = ( x , − x ̧ ) 2 + ( Y2 — Y2 ) 2 .. - - .. ( 1 ) , ( 2 ) . The student should draw figures placing P and Q in the different compartments and in different positions ; the equa ...
Σελίδα 8
... determined by giving to x and y values that satisfy the equation y - x - 2 = 0 ; such a line is called the locus of the equation . It will be shewn in the next chapter that the locus of the equation in question is a straight line . We ...
... determined by giving to x and y values that satisfy the equation y - x - 2 = 0 ; such a line is called the locus of the equation . It will be shewn in the next chapter that the locus of the equation in question is a straight line . We ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 100 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.