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 1
... parallel to OY meeting OX in M , and PN parallel to OX meeting OY in N. The position of P is evidently known if OM and ON are known ; for if through N and M lines be drawn parallel to OX and OY respectively , they will intersect in P ...
... parallel to OY meeting OX in M , and PN parallel to OX meeting OY in N. The position of P is evidently known if OM and ON are known ; for if through N and M lines be drawn parallel to OX and OY respectively , they will intersect in P ...
Σελίδα 4
... length of the line joining two points . P R X ' M N X Y ' Let P and Q be the two points ; @ the inclination of the axes OX , OY . Draw PM , QN parallel to OY ; let x , y , be the co - ordinates of P , and x , 4 CO - ORDINATES OF A POINT .
... length of the line joining two points . P R X ' M N X Y ' Let P and Q be the two points ; @ the inclination of the axes OX , OY . Draw PM , QN parallel to OY ; let x , y , be the co - ordinates of P , and x , 4 CO - ORDINATES OF A POINT .
Σελίδα 5
... parallel to OX . Then , by Trigonometry , PQ2 = PR2 + QR2 – 2PR . QR cos PRQ = PR + QR2 + 2PR . QR cos w . But PR = x - x1 , and QR = y , —y1 ; therefore PQ2 = ( x , − x ̧ ) 2 + ( y2 − y1 ) 2 + 2 ( x , − x1 ) ( y2 — y1 ) cos w ...
... parallel to OX . Then , by Trigonometry , PQ2 = PR2 + QR2 – 2PR . QR cos PRQ = PR + QR2 + 2PR . QR cos w . But PR = x - x1 , and QR = y , —y1 ; therefore PQ2 = ( x , − x ̧ ) 2 + ( y2 − y1 ) 2 + 2 ( x , − x1 ) ( y2 — y1 ) cos w ...
Σελίδα 6
... parallel to OX meeting CN in D. Let x , y be the co- ordinates of C. It is obvious from the figure that LN = AD AC = NM DR CB x that is , - X1 x2 - x = Similarly , n1x2 + n2x1 ..x = n1 + n2 192 y = n1 + n z In this article the axes may ...
... parallel to OX meeting CN in D. Let x , y be the co- ordinates of C. It is obvious from the figure that LN = AD AC = NM DR CB x that is , - X1 x2 - x = Similarly , n1x2 + n2x1 ..x = n1 + n2 192 y = n1 + n z In this article the axes may ...
Σελίδα 11
... parallel to either axis . Let ABD be a straight line meeting the axis of y in B. Draw a line OE through the origin parallel to ABD . In ABD take any point P ; draw PM parallel to OY , meeting OX in M and OE in Q. Suppose OB = c , and ...
... parallel to either axis . Let ABD be a straight line meeting the axis of y in B. Draw a line OE through the origin parallel to ABD . In ABD take any point P ; draw PM parallel to OY , meeting OX in M and OE in Q. Suppose OB = c , and ...
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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.