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 4
... referred to OX as the axis of x , and a line through O perpendicular to OX as the axis of y . Also let 0 and be the polar co - ordinates of P. If we draw from P a perpendicular on OX , we see that x = r cos 0 , and y = r sin 0 . These ...
... referred to OX as the axis of x , and a line through O perpendicular to OX as the axis of y . Also let 0 and be the polar co - ordinates of P. If we draw from P a perpendicular on OX , we see that x = r cos 0 , and y = r sin 0 . These ...
Σελίδα 23
... referred to rectangular co - ordinates . Let Ax + By + C = 0 be the equation to a line referred to rectangular co - ordinates . Put rcos for x , and r sin for y , Art . 8 ; thus Ar cos + Br sin 0 + C = 0 ........ ( 1 ) This equation may ...
... referred to rectangular co - ordinates . Let Ax + By + C = 0 be the equation to a line referred to rectangular co - ordinates . Put rcos for x , and r sin for y , Art . 8 ; thus Ar cos + Br sin 0 + C = 0 ........ ( 1 ) This equation may ...
Σελίδα 43
... 40 hold whether the axes are rectangular or oblique ; in Art . 33 , however , m must have that meaning which is required when the axes are oblique . To find the angle between two straight lines referred to OBLIQUE AXES . 43.
... 40 hold whether the axes are rectangular or oblique ; in Art . 33 , however , m must have that meaning which is required when the axes are oblique . To find the angle between two straight lines referred to OBLIQUE AXES . 43.
Σελίδα 44
Isaac Todhunter. To find the angle between two straight lines referred to oblique axes . Let be the angle between the axes ; y = mx + c , the equation to one line ; y = mx + c , the equation to the other . Let a ,, a , be the angles ...
Isaac Todhunter. To find the angle between two straight lines referred to oblique axes . Let be the angle between the axes ; y = mx + c , the equation to one line ; y = mx + c , the equation to the other . Let a ,, a , be the angles ...
Σελίδα 54
... referred to oblique axes . 23. Shew that whether the axes be rectangular or oblique the lines y + x = 0 and y - x = 0 are at right angles . 24. Given the lengths of two sides of a parallelogram and the angle between them , write down ...
... referred to oblique axes . 23. Shew that whether the axes be rectangular or oblique the lines y + x = 0 and y - x = 0 are at right angles . 24. Given the lengths of two sides of a parallelogram and the angle between them , write down ...
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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.