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a2 sin2 abscissa asymptotes axes axis of x becomes bisect the angles centre chord of contact circle conic section conjugate diameters conjugate hyperbola constant corresponding cos2 denote determined directrix ellipse equa equal excentricity expression external point find the equation find the locus fixed point focal chord focus given point given straight line Hence the equation inclined latus rectum length Let the equation line drawn line joining line meets lines represented lines which pass major axis meet the curve middle point negative normal oblique obtain ordinate parabola parallelogram perpendicular point h point of intersection polar co-ordinates polar equation pole positive preceding article proposition prove radical axis ratio rectangular required equation respectively right angles satisfy shew shewn sides Similarly straight line passing suppose tangents are drawn tion trapezium triangle vertex zero
Página 187 - 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.
Página 98 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
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 139 - 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 32 - To find the equations to the straight lines which pass through a given point and make a given angle with a given straight line.
Página 266 - S through which any radius vector is drawn meeting the curves in P, Q, respectively. Prove that the locus of the point of intersection of the tangents at P, Q, is a straight line. Shew that this straight line passes through the intersection of the directrices of the conic sections, and that the sines of the angles which it makes with these lines are inversely proportional to the corresponding excentrities.
Página 10 - Art. 11 so as to give an expression for the area of a triangle in terms of the polar co-ordinates of its angular points.