6. Distance between two points (~1 y1) and (x2 Y2) = (x1 x2)2 + (Y1 — Y2)2. EQUATIONS TO THE STRAIGHT LINE. Where a and b are its intercepts on the axes of x and its perpendicular distance from the origin. 7. y. a the inclination of p to the axis of x, or to the initial line, and B its inclination to the axis of y. m the tangent of the angle which it makes with the positive part of the axis of x. n the ratio of the sines of the angles which it makes with the axes of x and y. = mx + b 8. 1 = a b Rectangular co-ordinates. Oblique co-ordinates. 12. x cos a + y cos B 13. = p p = p sec (0− a) Polar co-ordinates. FORMS OF CERTAIN LINES REFERRED TO 14. Line through origin, 17. Line through (11) and making an angle tan-1 t with the line y = mx + b, 18. For intersection of lines y = mx + b, 22. Perpendicular from (~11) on the line y 1 m' THE CIRCLE. (r = radius). 23. Equation to the circle, centre being origin, 24. General equation, h and k being co-ordinates of centre, 25. Equation to tangent at point (x'y'), THE PARABOLA. Focus S. Vertex A. AS = α. 27. Equation to parabola, vertex being origin, y2 = 4ax. 28. Equation to parabola, origin being point (k, h) in the 29. Polar equation to parabola, focus being pole, 30. Equation to parabola referred to any diameter and tangent at its extremity (P). PV, QV being co-ordinates of any point Q, QV2 = 4SP. PV. 31. Equation to tangent at point (x'y'), 32. Equation to normal through (x'y'), General Properties of the Parabola. 33. Any point P is equidistant from focus and directrix. 38. Subtangent Subnormal SY2 = = 2x. = 2a. SP. SA where SY I tangent at P. 39. A diameter and the focal distance of its extremity make equal angles with the tangent at the same point. 40. Tangents at the extremity of any focal chord intersect at right angles in the directrix. = THE ELLIPSE. = 2a. Axis Centre C. Foci S and H. Axis major ACA' minor BCB' 26. I the intersection of the axis major with the directrix. Eccentricity = e. 41. Equation to the ellipse, centre being origin, 42. Equation to the ellipse, vertex A being origin, 43. Polar equation to the ellipse, centre being pole, 44. Polar equation to the ellipse, focus S being pole, e2) 1 e cos e 45. Equation to the ellipse referred to conjugate diameters CP, CD; CV, QV being co-ordinates of Q, 46. Equation to tangent at point (x'y'), 47. Equation to normal through (x'y'), General Properties of the Ellipse. Focal distance of point P Distance of P from the directrix 48. = constant 58. The normal at any point bisects the angle between the focal distances of that point. 62. The tangents at the extremities of any focal chord intersect in the directrix. 63. The tangent at the extremity of any diameter is parallel to the corresponding conjugate diameter. THE HYPERBOLA. Centre C. Foci S and H. Transverse axis A CA' = 2 a. Conjugate axis BCB' 2 b. Eccentricity = e. = 64. Equation to the hyperbola, centre being origin, |