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analytically angle approaches asymptotes axes becomes bisectors bisects called centre chapter chord circle circle x▓ condition conic section conjugate diameters constant co÷rdinates corresponding curve cuts determined diameter directrix distance draw drawn eccentricity ellipse equal example extremities factors Find the equation fixed focal foci focus formulas given given line given point Hence hyperbola imaginary intercept length limiting line joining line passing loci locus m₁ meet method middle point moves negative normal NOTE numerical obtain origin P₁ pair parabola parallel passing perpendicular plane plot point of intersection polar pole positive Prove radical radius represents respectively satisfy Show sides slope solve square straight line Substituting tangent tion transformation transverse axis triangle true values vertex vertices whence written y₁ zero
Page 229 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 133 - A conic section is the locus of a point which moves so that its distance from a fixed point, called the focus, is in a constant ratio to its distance from a fixed straight line, called the directrix.
Page 23 - ... four times the square of the line joining the middle...
Page 132 - 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. Show that the locus is a circle. 50. Prove that the two circles z2 + y2 + 2 G,z + 2 Ftf + Cj = 0 and x2 + y...
Page 23 - The sum of the squares of the other two sides is equal to twice the square of half the base, plus twice the square of the median.
Page 23 - Prove analytically that in any right triangle the straight line drawn from the vertex to the middle point of the hypotenuse is equal to one half the hypotenuse.
Page 86 - Prove analytically that the medians of a triangle meet in a point. 71. Prove analytically that the perpendicular bisectors of the sides of a triangle meet in a point. 72. Prove analytically that the perpendiculars from the vertices of a triangle to the opposite sides meet in a point.
Page 326 - The coordinates of the vector in the ox'y' system are (x',y') and, furthermore, as may be verified, x' = x cos 6 + y sin 6 y