Cartesian Plane Geometry, Volume 1 |
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Common terms and phrases
2hxy a² b2 a²m² algebraic am² asymptotes ax² axes by² central conic centre coefficients common points condition conjugate diameters conjugate hyperbolas conjugate with respect constant diagram directrix distance ellipse equal equation for intersections expression Find the coordinates Find the equation Find the locus Find the tangents fixed point foci geometrical give harmonic conjugates Hence the equation imaginary infinity isotropic lines latus rectum lies line-equation lines that join m₁ major axis meets the curve negative normal obtain ordinates origin pair parabola y² parallel perpendicular point at infinity point of bisection point of contact point of intersection pole positive Prove quadratic quadratic equation ratio represents respect to x² right angles second degree Show side slope straight line triangle values vertex x₁ y₁ y₁²
Popular passages
Page 109 - 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 236 - The parabola is the locus of a point whose distance from a fixed point, the focus, is always equal to its distance from a fixed line, the directrix.
Page 121 - PF'/PH'= e, by the definition of the curve. Furthermore :J (b) \PF—PF'\=2a. In fact, the hyperbola is often defined as the locus of a point which moves so that the difference of its distances from two fixed points is constant.
Page 121 - 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.
Page 95 - PF'/PH' = e, by definition of the curve. Furthermore :f (6) PF + PF' = 2a. In fact, the ellipse is often defined as the locus of a point which moves so that the sum of its distances from two fixed points is constant.
Page 33 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 109 - ... line. The fixed point is called the focus, the fixed line is called the directrix; the constant ratio is called the eccentricity, and is denoted by e.
Page 409 - The foot of the perpendicular from the focus of a parabola to a tangent lies on the tangent at the vertex.
Page 94 - What is the locus of a point which moves so that the square of its distance from a fixed point is proportional to its distance from a fixed line?