A Treatise on Plane Co-ordinate Geometry as Applied to the Straight Line and the Conic SectionsMacmillan, 1862 - 326 páginas |
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Página 1
... respectively , they will intersect in P. The point O is called the origin ; the lines OX and OY are called axes ; OM is called the abscissa of the point P ; and . T. C. S. 1 ON , or its equal MP , is called the PLANE CO-ORDINATE ...
... respectively , they will intersect in P. The point O is called the origin ; the lines OX and OY are called axes ; OM is called the abscissa of the point P ; and . T. C. S. 1 ON , or its equal MP , is called the PLANE CO-ORDINATE ...
Página 14
... respectively . Suppose OA = a , OB = b . Let P be any point in the line ; x , y its co - ordinates ; draw PM parallel to OY . Then by similar triangles , that is , PM AM OB AO ; 210 = 818 = α -x + α 볼 = 1 . 18. It will be a useful ...
... respectively . Suppose OA = a , OB = b . Let P be any point in the line ; x , y its co - ordinates ; draw PM parallel to OY . Then by similar triangles , that is , PM AM OB AO ; 210 = 818 = α -x + α 볼 = 1 . 18. It will be a useful ...
Página 22
... respectively cos a and sin a , that is , the cosines of the inclinations of the line to the axes of x and y respectively . In the preceding figure P falls to the right of Q and x - h is positive . If P were to the left of Q then x - h ...
... respectively cos a and sin a , that is , the cosines of the inclinations of the line to the axes of x and y respectively . In the preceding figure P falls to the right of Q and x - h is positive . If P were to the left of Q then x - h ...
Página 28
... respectively . Thus the equation informs us that the area of the triangle formed by joining ( x , y ) , ( x1 , y1 ) , ( x ,, y2 ) vanishes , as should evidently be the case since the vertex ( x , y ) falls on the base , that is , on the ...
... respectively . Thus the equation informs us that the area of the triangle formed by joining ( x , y ) , ( x1 , y1 ) , ( x ,, y2 ) vanishes , as should evidently be the case since the vertex ( x , y ) falls on the base , that is , on the ...
Página 29
... respectively y = m1x + c1 y = mx + c2 ( 1 ) , ( 3 ) . y = m2x + c2 ( 2 ) , ...... The co - ordinates of the point of intersection of ( 1 ) and ( 2 ) are 1 x = C - Ca m2 - m1 9 y = c1m2 - c2m1 m2 - m1 If the third line passes through the ...
... respectively y = m1x + c1 y = mx + c2 ( 1 ) , ( 3 ) . y = m2x + c2 ( 2 ) , ...... The co - ordinates of the point of intersection of ( 1 ) and ( 2 ) are 1 x = C - Ca m2 - m1 9 y = c1m2 - c2m1 m2 - m1 If the third line passes through the ...
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Términos y frases comunes
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
Pasajes populares
Página 100 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Página 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.
Página 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.
Página 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.
Página 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.