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
... rectangular . If the angle YOX be not a right angle , the axes are called oblique . All that has been hitherto said applies whether the axes are rectangular or oblique . We shall always suppose the axes rectangular unless the contrary ...
... rectangular . If the angle YOX be not a right angle , the axes are called oblique . All that has been hitherto said applies whether the axes are rectangular or oblique . We shall always suppose the axes rectangular unless the contrary ...
Σελίδα 4
... rectangular and polar co - ordi- nates of a point . From them , or from the figure , we may deduce x2 + y2 = r2 , y = = tan 0 . x 9. We proceed to investigate expressions for some geome- trical quantities in terms of co - ordinates . To ...
... rectangular and polar co - ordi- nates of a point . From them , or from the figure , we may deduce x2 + y2 = r2 , y = = tan 0 . x 9. We proceed to investigate expressions for some geome- trical quantities in terms of co - ordinates . To ...
Σελίδα 5
... 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- tions ( 1 ) and ( 2 ) will be ...
... 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- tions ( 1 ) and ( 2 ) will be ...
Σελίδα 6
... rectangular . A simple case is that in which we require the co - ordinates of the point midway between two given points ; then n1 = n , and x = √ ( x1 + x ̧ ) , y = + ( y1 + y2 ) . 11. To express the area of a triangle in terms 6 CO ...
... rectangular . A simple case is that in which we require the co - ordinates of the point midway between two given points ; then n1 = n , and x = √ ( x1 + x ̧ ) , y = + ( y1 + y2 ) . 11. To express the area of a triangle in terms 6 CO ...
Σελίδα 9
... rectangular co - ordinates of the points whose polar co - ordinates are ( 1 ) 0 = r = 3 ; П ( 2 ) 0 = - , r = 3 ; 3 π 3 ( 3 ) 0 = , r = −3 ; and indicate the points in a figure . 3. The co - ordinates of P are 3 and 7 ; find the length ...
... rectangular co - ordinates of the points whose polar co - ordinates are ( 1 ) 0 = r = 3 ; П ( 2 ) 0 = - , r = 3 ; 3 π 3 ( 3 ) 0 = , r = −3 ; and indicate the points in a figure . 3. The co - ordinates of P are 3 and 7 ; find the length ...
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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.