## An Elementary Treatise on Analytical Geometry: With Numerous Examples |

### Other editions - View all

An Elementary Treatise on Analytical Geometry: With Numerous Examples W. J. Johnston No preview available - 2018 |

An Elementary Treatise on Analytical Geometry: With Numerous Examples (1893) W. J. Johnston No preview available - 2008 |

### Common terms and phrases

asymptotes ax² axes bisected bisectors by² centre chord circle x² co-ord's co-ordinates confocal conic conjugate hyperbola constant cos² curve determined director circle directrix ellipse envelope eq'n Find locus Find the equation find the locus fixed point foci focus given line given point inscribed intercepts inters'n intersection isotropic lines join latus rectum line at infinity line-pair m₁ meet mid point nine-point circle normal Note-Let Note-The origin parabola parallel passes perpendicular points of contact polar prove quadratic quadrilateral r₁ radical axis radius ratio rectangular hyperbola represents required equation right angles Show sides sin² straight line tangent tangent at x'y theorem touch triangle ABC triangle of reference vertex vertices X₁ x²/a² Y₁ y²/b²

### Popular passages

Page 128 - Find the locus of a point, the distances of which from two given straight lines have a fixed ratio. 143. 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 81 - 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 208 - 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 405 - The diagonals of a quadrilateral inscribed in a circle intersect at right angles...

Page 1 - THE Rectangle under the Sum and Difference of two Lines, is equal to the Difference of the Squares, of those Lines.

Page 352 - Two circles have double internal contact with an cllipse,t and a third circle passes through the four points of contact. If t, t', T be the tangents' from any point on the ellipse to these three circles, prove that T* = «'. 579.

Page 158 - 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?

Page 105 - A straight line moves so that the sum of the reciprocals of its intercepts on two fixed intersecting lines is constant; shew that it passes through a fixed point. 2. Prove that bx" — 2/ixy + ay* = 0 represents two straight lines at right angles respectively to the straight lines ax1 + 2hxy + by*=Q.

Page 425 - Edition. 8vo, 1 2*. 6d. Graphical Statics. Two Treatises on the Graphical Calculus and Reciprocal Figures in Graphical Statics. By the same Author. Translated by T. HUDSON BEARS.