Analytic GeometryD.C. Heath & Company, 1915 - Geometry, Analytic |
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Common terms and phrases
9 y² a² b2 a²b² a²y² abscissa analytic geometry angle asymptotes b²x² called circle common chord conic conjugate hyperbolas constant coördinate axes cos² cosines curve cycloid defined Derive the equation determined directrix distance draw ellipse equa Exercise Find the coördinates Find the equation Find the locus fixed point focal radii foci focus formula generatrix geometric given equation Hence intercept form latus rectum length limaçon linear equations logarithmic origin P₁ pair parabola parameter parametric equations passing perpendicular polar axis polar coördinates positive principal axis Problem Prove radical axis radius rectangular coördinates rotation Show sin² slope Solution Solving standard form straight line Substituting subtangent surface surface of revolution symmetrical with respect symmetry table of values tangent theorem tion transform triangle variables vertex vertices Write the equations x-axis x₁ y-axis y-intercept y₁
Popular passages
Page 88 - Show that the locus of a point which moves so that the sum of its distances from two h'xed straight lines is constant is a straight line.
Page 16 - The sum of the squares of the four sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the mid-points of the diagonals.
Page 174 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 75 - Conic, is the locus of a point which moves so that its distance from a fixed point is in a constant ratio to its distance from a fixed straight line.
Page 16 - In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of ' one of those sides and the projection of the other side upon it.
Page 25 - A point moves so that the sum of the squares of its distances from the sides of an equilateral triangle is constant.
Page 99 - The hyperbola is a plane curve generated by a point moving so that the difference of its distances from two fixed points, called the "focuses,
Page 47 - The perpendicular bisectors of the sides of a triangle meet in a point. 12. The bisectors of the angles of a triangle meet in a point. 13. The tangents to a circle from an external point are equal. 14...
Page 16 - The sum of the squares of the four sides of a parallelogram is equal to the sum of the squares of the diagonals.
Page 16 - THEOREM 422. In any triangle the sum of the squares of two sides is equal to twice the square of half the third side, increased by twice the square of the median on that side.