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 57
... described , having their sides parallel to two given lines , the other diagonals of the parallelograms will meet in a point . 45. If from a fixed point O a straight line be drawn OABCD ... meeting in A , B , C , D , ... any given fixed ...
... described , having their sides parallel to two given lines , the other diagonals of the parallelograms will meet in a point . 45. If from a fixed point O a straight line be drawn OABCD ... meeting in A , B , C , D , ... any given fixed ...
Página 99
... described ; find its equation . 6. A and B are two fixed points , and P a point such that AP = mBP , where m is a constant ; shew that the locus of P is a circle , except when m = 1 . 7. The locus of the point from which two given ...
... described ; find its equation . 6. A and B are two fixed points , and P a point such that AP = mBP , where m is a constant ; shew that the locus of P is a circle , except when m = 1 . 7. The locus of the point from which two given ...
Página 137
... described on SP as diameter . 35 . Shew that the circle described on SP as diameter touches the tangent at the vertex . 36. If the line y = m ( x - a ) meets the parabola in ( x ' , y ' ) and ( x " , y ' ) , shew that 4a x2 + x " = 2a + ...
... described on SP as diameter . 35 . Shew that the circle described on SP as diameter touches the tangent at the vertex . 36. If the line y = m ( x - a ) meets the parabola in ( x ' , y ' ) and ( x " , y ' ) , shew that 4a x2 + x " = 2a + ...
Página 138
... described through these three points passes through the vertex of the parabola . 29 45. If two of the normals which can be drawn to a para- bola through a point are at right angles , the locus of that point is a parabola . 46. If two ...
... described through these three points passes through the vertex of the parabola . 29 45. If two of the normals which can be drawn to a para- bola through a point are at right angles , the locus of that point is a parabola . 46. If two ...
Página 139
... described upon a chord of a parabola as diameter just touches the axis ; shew that if 0 be the inclina- tion of the chord to the axis , 4a the latus rectum of the parabola , and c the radius of the circle , 2a tan 0 = 53. If 0 , 0 ' be ...
... described upon a chord of a parabola as diameter just touches the axis ; shew that if 0 be the inclina- tion of the chord to the axis , 4a the latus rectum of the parabola , and c the radius of the circle , 2a tan 0 = 53. If 0 , 0 ' be ...
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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.