A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and the Conic SectionsMacmillan, 1862 - 326 σελίδες |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 12
... Hence if the line through the origin parallel to the given line falls between OY and OX , m is the tangent of an acute angle and is positive ; if between OY and OX produced to the left , m is the tangent of an obtuse angle and is ...
... Hence if the line through the origin parallel to the given line falls between OY and OX , m is the tangent of an acute angle and is positive ; if between OY and OX produced to the left , m is the tangent of an obtuse angle and is ...
Σελίδα 13
... Hence calling y the ordinate of any point P , we have for the equation to the line y = b . Next suppose the line parallel to the axis of y . Let AD be the line meeting the axis of x in A ; suppose OA = a . Since the line is parallel to ...
... Hence calling y the ordinate of any point P , we have for the equation to the line y = b . Next suppose the line parallel to the axis of y . Let AD be the line meeting the axis of x in A ; suppose OA = a . Since the line is parallel to ...
Σελίδα 15
... hence the point which has its abscissa = 1 and its ordinate = 2 is on the line . Again , suppose x = 2 , then y ; the point which has its abscissa = 2 and its ordinate is therefore on the line . Join the two points thus determined and ...
... hence the point which has its abscissa = 1 and its ordinate = 2 is on the line . Again , suppose x = 2 , then y ; the point which has its abscissa = 2 and its ordinate is therefore on the line . Join the two points thus determined and ...
Σελίδα 16
... Hence this equation represents a line through O bisecting the angle between OY and OX pro- duced to the left in the figure to Art . 14 . 19. The student is recommended to make himself tho- roughly acquainted with the previous Articles ...
... Hence this equation represents a line through O bisecting the angle between OY and OX pro- duced to the left in the figure to Art . 14 . 19. The student is recommended to make himself tho- roughly acquainted with the previous Articles ...
Σελίδα 27
... hence m = x2 - x1 Substitute the value of m in ( 4 ) and we have for the required equation = y - y1 Y2 - yi x - x1 - ( x − x1 ) ( 5 ) . We may also write the equation thus , - ( x , — x ̧ ) ( y — y ̧ ) = ( Y2 — Y1 ) ( x — x ̧ ) ...
... hence m = x2 - x1 Substitute the value of m in ( 4 ) and we have for the required equation = y - y1 Y2 - yi x - x1 - ( x − x1 ) ( 5 ) . We may also write the equation thus , - ( x , — x ̧ ) ( y — y ̧ ) = ( Y2 — Y1 ) ( x — x ̧ ) ...
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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.