Curve surface of cone = πrl; = slant height. Curve surface of frustum of cone = π (r1+r2)l Curve surface of segment of sphere 2rrh; h = height of segment. Curve surface of spherical zone = 2xrh; h = height of h, perpendicular height; A, d areas of ends. πλ Volume of segment of sphere = (h2 + 3r2), r being 6 radius of base, h, the height, of the segment; or r being radius of sphere; h, height of segment. πη h2 Volume of zone of sphere = {μ3+3 (p2+q2)} 6 P, q being radii of ends. FORMULE IN CO-ORDINATE GEOMETRY. Equation to straight line, axes rectangular, y = mx + c. Equation to straight line, axes rectangular, through (x, y), y—y' = m (x − x′). Equation to straight line, axes rectangular, through (x, y) and (x", y"); y-y' = y"-y' (x-x'). Equation to straight line, axes rectangular, through (x, y) & L to y=mx+c; y-y' 1 m -(x-x'). x Equation in terms of the intercepts of the axes, +2/ Equation in terms of perpendicular from origin, x cos a + y sin a — p = 0. Equation when the axes are oblique, y = Condition of perpendicularity of a = 1. y = mx + c and y = mx + c1 ; mm1 = Length of perpendicular, from (x', y') upon y = mx + c = ± Length of perpendicular, from y' - mx'. -c √1+ m2 1. (x, y) upon x cos a+y sin a-p,=x' cos a+y' sin a— -p. Equation to circle, origin anywhere, (x−a)2 + (y—b)2 = r2. Equation to circle, origin at centre, x2 + y2 = r2. Equation to tangent at (x', y'), xx' + yy' = r2; y = mx + r√ 1 + m2. Equation to normal at (x', y′), y = 2.x. Equation to chord of contact, xh + yk = r2. Equation to parabola, origin at vertex, y2 = 4ax. Equation to tangent at (x', y'), yy'=2a (x+x'); y=mx+ Equation to normal at (x', y'), y-y' or y = mx-2am-am3. Equation to tangent at (x', y'), a2yy' +b2xx'=a2b2, or y = mx + √ a2 m2 + b2. Equation to tangent at (x', y'), a2yy' — b2xx' — — a2b2, Equation to normal at (x', y'), y-y' = Polar equation to straight line, pr cos (0-a). Polar equation to circle, c2: = r2 + 12 — 2lr cos (6—a). Polar equation to parabola, focus, the pole, r = 2a 1 + cos α m |