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 3
... similar convention to that in Art . 4 ; angles measured in one direction from OX are con- sidered positive and in the other negative . Thus if in the figure XOP be a positive angle , XOQ will be a negative angle ; if the angle XOQ be a ...
... similar convention to that in Art . 4 ; angles measured in one direction from OX are con- sidered positive and in the other negative . Thus if in the figure XOP be a positive angle , XOQ will be a negative angle ; if the angle XOQ be a ...
Σελίδα 14
... similar triangles , that is , PM AM OB AO ; 210 = 818 = α -x + α 볼 = 1 . 18. It will be a useful exercise for the student to draw the straight lines corresponding to some given equations . Thus suppose the equation 2y + 3x = 7 proposed ...
... similar triangles , that is , PM AM OB AO ; 210 = 818 = α -x + α 볼 = 1 . 18. It will be a useful exercise for the student to draw the straight lines corresponding to some given equations . Thus suppose the equation 2y + 3x = 7 proposed ...
Σελίδα 39
... x cos a + y sin a - p = 0 , 2 and cos α = - sin a = - 3 √13 √13 , P = 4 √13 In this example a is an angle lying between π and 3п 2 Any other example may be treated in a similar manner- RULE FOR TRANSFORMING AN EQUATION . 39.
... x cos a + y sin a - p = 0 , 2 and cos α = - sin a = - 3 √13 √13 , P = 4 √13 In this example a is an angle lying between π and 3п 2 Any other example may be treated in a similar manner- RULE FOR TRANSFORMING AN EQUATION . 39.
Σελίδα 40
Isaac Todhunter. Any other example may be treated in a similar manner- the rule being the following . Collect the terms on one side , and if necessary , change the signs so that the equation may be in the form Ax + By - C = 0 , where C ...
Isaac Todhunter. Any other example may be treated in a similar manner- the rule being the following . Collect the terms on one side , and if necessary , change the signs so that the equation may be in the form Ax + By - C = 0 , where C ...
Σελίδα 63
... Similar results follow from the second of equations . ( 2 ) , and from the third of equations ( 2 ) . Hence in this case if equations ( 2 ) are satisfied , the three given lines either meet in a point or are parallel . 1 И = ' Then Next ...
... Similar results follow from the second of equations . ( 2 ) , and from the third of equations ( 2 ) . Hence in this case if equations ( 2 ) are satisfied , the three given lines either meet in a point or are parallel . 1 И = ' Then Next ...
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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.