Coordinate geometry Summary, Lecture notes of Geometry

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PURE 3 Coordinate Geomelry. 4) Straight lines “gradient of AB = Ys 7 Yo vse xy ue B lary.) - “lng of AB Sta) * (ye -y? Pythagoras’ tKeorem. * midpoint of AB > (sem, es ) a a * parallel lines —* some gradient * perpendicular lines « gradient =m, Alenys) © gradient mm, pass through point (x,y) & equation: y-y, + m(x-x.) 2. Circles % Guy) center Cx, y) (_\ . _ LT Pore f y * center Ca, b) Pix yy * radus or equation of a circle: 4) completed square form ° d Expanding. (x-a)*+ (y-b)** r* gives: x dow ta’ + y* dby + yh ar® Reawrange x + y~ don - Dby + (ae b*- 1?) +0 “+ 2) equation of circle in expandecl form ety s dpe t ofp +e 0 > enter (-g, -f) + dus ght foe