Algebraic Geometry: A New Treatise on Analytical Conic Sections

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G. Bell & sons, 1906 - 325 páginas
 

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Página 46 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Página 98 - A point moves so that the sum of the squares of its distances from the sides of an equilateral triangle is constant.
Página 300 - 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 119 - 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 45 - K, x and y instead of a and (i, we have for the equation of its locus (3) Through a fixed point O any straight line is drawn meeting two given parallel straight lines in P and Q; through P and Q straight lines are drawn in fixed directions, meeting in B : prove that the locus of E is a straight line.
Página 45 - Find the locus of a point which moves so that the sum of its distances from two vertices of an equilateral triangle shall equal its distance from the third.
Página 268 - D' is a right angle, and the angle DPF = DPD', and PF = PD', .-. DFP is a right angle. In like manner, DFP' is a right angle ; hence, first, the part of the tangent intercepted between the point of contact and the directrix, subtends a right angle at the focus ; second, the line joining the points of contact of perpendicular tangents always passes through thefocut.
Página 14 - What is the equation of the locus of a point which moves so...
Página 97 - A point moves so that the square of its distance from the base of an isosceles triangle is equal to the product of its distances from the other two sides.
Página 132 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.

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