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 10
... shew that the polar co - ordinates 2rr , cos ( 0,0 ) of Care 0 = ( 0 , + 02 ) and r = 12 11. Find the value of CD and AD in question 8 in terms of the co - ordinates there used ; and shew that AC2 + BC2 = 2 CD2 + 2AD2 . 12. Find the ...
... shew that the polar co - ordinates 2rr , cos ( 0,0 ) of Care 0 = ( 0 , + 02 ) and r = 12 11. Find the value of CD and AD in question 8 in terms of the co - ordinates there used ; and shew that AC2 + BC2 = 2 CD2 + 2AD2 . 12. Find the ...
Página 13
... shew that any equation of the first degree with two variables represents a straight line . The general equation of the first degree with two variables is of the form Ax + By + C = 0 ........ A , B , C being finite or zero . . ( 1 ) ...
... shew that any equation of the first degree with two variables represents a straight line . The general equation of the first degree with two variables is of the form Ax + By + C = 0 ........ A , B , C being finite or zero . . ( 1 ) ...
Página 18
... shew the agreement of the equations in Arts . 14 , 17 , 20 , or from one of them deduce the others . 22. The student may exercise himself by varying the figures which we have used in investigating the equations . Thus , for example , in ...
... shew the agreement of the equations in Arts . 14 , 17 , 20 , or from one of them deduce the others . 22. The student may exercise himself by varying the figures which we have used in investigating the equations . Thus , for example , in ...
Página 53
... Shew what loci are represented by the equations ( 2 ) x2 - y1 = 0 , ( 3 ) x2 + xy = 0 , ( 4 ) xy = 0 , ( 5 ) x2 + y2 + a2 = 0 , ( 6 ) x ( y - a ) = 0 . 16. Interpret ( 1 ) ( x - a ) EXAMPLES ON THE STRAIGHT LINE . 53.
... Shew what loci are represented by the equations ( 2 ) x2 - y1 = 0 , ( 3 ) x2 + xy = 0 , ( 4 ) xy = 0 , ( 5 ) x2 + y2 + a2 = 0 , ( 6 ) x ( y - a ) = 0 . 16. Interpret ( 1 ) ( x - a ) EXAMPLES ON THE STRAIGHT LINE . 53.
Página 54
... Shew that 3y- 8xy - 3x2 + 30x270 represents two straight lines at right angles to one another . 19. Find the equations to the diagonals of the four - sided figure , the sides of which are represented by the equations x = 4 , y = 5 , y ...
... Shew that 3y- 8xy - 3x2 + 30x270 represents two straight lines at right angles to one another . 19. Find the equations to the diagonals of the four - sided figure , the sides of which are represented by the equations x = 4 , y = 5 , y ...
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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.