Elements of Analytic Geometry |
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a² b2 a²b² abscissa Analytic Geometry asymptotes auxiliary circle axes of co-ordinates axis of x b²x² bisectors bisects all chords By² called centre chords parallel circle x² coincide conjugate diameters conjugate hyperbola constant Construct cos² denote directrix ellipse equa equal equidistant equilateral hyperbola Find the distance Find the equation Find the length Find the locus fixed point focal radii foci focus Geometry given equation given line given point Hence imaginary intercepts intersection latus rectum line Ax+By+C=0 loci m²a² major axis middle point negative normal obtain ordinate origin parabola y² perpendicular point h point of contact polar equation pole positive Prove quadrant radical axis radius rectangular represent respect sides solving straight line passing substitution subtangent supplementary angle tangents drawn tion triangle values variable vertex vertices whence x₁ y₁ Y₂ zero
Popular passages
Page 33 - A point moves so that the sum of the squares of its distances from the four sides of a square is constant.
Page 173 - F') ; the diameter drawn through them is called the major axis, and the perpendicular bisector of this diameter the minor axis. It is also defined as the locus of a point which moves so that the ratio of its distance from a fixed point...
Page 203 - 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 200 - 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.
Page 145 - An ellipse is the locus of a point, the sum of whose distances from two fixed points is constant. In Fig. 10.12, the two fixed points are labeled F and F' and are termed the foci of the ellipse, with x coordinates /and/+ 2c.
Page 136 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 54 - ... lines, and the perpendiculars from the three vertices of the triangle upon this line will be equal, by Chap. I, II, 13. A perpendicular to AB erected midway between any two of these three is perpendicular to the corresponding side of the triangle at its middle point (Chap.
Page 65 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Page 119 - A parabola is the locus of a point whose distance from a fixed point is always equal to its distance from a fixed line.
Page 180 - Find the locus of a point the sum of whose distances from two given parallel lines is equal to a given length.