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Coordinate Geometry FormulasCoordinate Geometry Formulas "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #2 20060402 16:48:57
Re: Coordinate Geometry FormulasStraight line Slope of a line passing through is given by The equation of a straight line passing through is given by Character is who you are when no one is looking. #3 20060409 16:42:40
Re: Coordinate Geometry FormulasDistance between two points. and is given by The distance of a point (x,y) from the origin is given by Character is who you are when no one is looking. #4 20060409 17:29:20
Re: Coordinate Geometry FormulasSection formula in the ratio m:n internally is The point which divides the line joining two points in the ratio m:n externally is The point which bisects the line joining two points is Area of a triangle The area of the triangle formed by the three points is given by . The three points are collinear if the area of the triangle formed is zero. If the three vertices of a triangle are Coordinates of the Cetroid: (The meeting pint of the three medians) If for the above said triangle, the lengths of the three sides of the triangle are a,b, and c, Cordinates of the Incentre: (The centre of a circle which touches the sides of a triangle, also the point of interesction of the angle bisectors of the triangle) Character is who you are when no one is looking. #5 20060416 01:37:07
Re: Coordinate Geometry FormulasConcurrent lines Angle between two lines Let the two lines make angles with the positive x axis. Then, . The angle between the lines is given by For parallel lines, and for perpendicular lines, The angle between the lines is given by If the lines are parallel, . If the lines are perpendicular to each other, Perpendicular distance from origin The perpendicular distance from the origin to the line ax+by+c=0 is Perpendicular distance of a line from a point The perpendicular distance from the point to the line ax+by+c=0 is given by Character is who you are when no one is looking. #6 20060416 17:05:44
Re: Coordinate Geometry FormulasCircle The equation of a circle whose centre is the origin and whose radius is a is given by the equation The general equation of a circle is where the centre is (g,f) and radius is The equation of a circle whose one diameter is the line segment joining the points is given by The equation represents a real circle if a point circle (a circle of zero radius) if and an imaginary circle if Character is who you are when no one is looking. #7 20060422 19:58:32
Re: Coordinate Geometry FormulasCircle through three points the equation of the circle passing through the three points is Character is who you are when no one is looking. #8 20060511 01:41:39
Re: Coordinate Geometry FormulasArea of a Quadrilateral is given by Character is who you are when no one is looking. #9 20060514 00:42:42
Re: Coordinate Geometry FormulasConics The coordinates of the focus are (a,0) and the vertex of the parabola is (0,0), the curve is symmetric about the xaxis. Equation of the tangent at (x1, y1) Condition that y=mx+c may be a tangent: The point of contact is Latus rectum = 4a Eccentricity, e=1 Equation of directrix, x=e. Equation of normal at (x1, y1): Equation of chord of contact of tangents drawn from (x1,y1): Parametric Representation The coordinates (at², 2at) satisfies the equation y²=4ax. The equation of the chord joining the points t1 and t2 on the parabola y²=4ax is The equation of the tangent at (at², 2at) is The equation of the normal at (at², 2at) is The point of intersection of tangents at t1 and t2 is Ellipse Standrad form: The coordinates of the foci are (ae, 0) and (ae, 0). Tangent at (x1,y1) Condition that y=mx+c may be a tangent: Latus rectum : Eccentricity, Equation of directrices: Equation of normal at (x1, y1): Equation of chord of contact of tangents drawn from (x1, y1): Parametric Representation x=acosθ, y=bsinθ satisifies the equation of the ellipse. The equation of the tangent at θ is The equation of normal at θ is Hyperbola Standard form: Tangent at (x1, y1): Condition that y=mx+c may be a tangent: Latus rectum : Eccentricity, e Equation of directrices: Equation of normal at (x1, y1): Equation of chord of contact of tangents drawn from (x1,y1): An asymptote of a hyperbola is a straight line which touches the hyperbola at infinity but does not lie altogether at infinity. The equations of asymptotes of a hyperbola are Parametric Representation x=asecθ, y=btanθ satisifies the equation of the hyperbola. The equation of the tangent at θ is The equation of the normal at θ is Rectangular Hyperbola A hyperbola in which b=a is called a Rectangular hyperbola. The asymptotes of a rectangular hyperbola are at right angles to each other. The asymptotes of a Rectangular Hyperbola are Standard form: Tangent at (x1, y1): Latus rectum = 2a Eccentricity, e= √2 Equation of normal at (x1, y1): Equation of chord of contact of tangents drawn from (x1, y1): Parametric form The point satisifes the equation of the rectangular hyperbola, The equation of the tangent at t is The equation of the normal at t is Character is who you are when no one is looking. #10 20060519 00:47:02
Re: Coordinate Geometry FormulasEquation of a plane Character is who you are when no one is looking. #11 20060611 00:35:00
Re: Coordinate Geometry FormulasAngle between two planes Character is who you are when no one is looking. #12 20060611 01:02:13
Re: Coordinate Geometry FormulasPerpendicular distance from a point to a plane The perpendicular distance from the origin to the plane Ax+By+Cz+D=0 is Character is who you are when no one is looking. #13 20060806 12:08:36
Re: Coordinate Geometry FormulasTranslation of Axes or Rotation of Axes The coordinates (x', y') of a coordinate system with origin (0, 0) with the x'axis making an angle of α with the positive xaxis are related to the standard (x, y) coordinates by the transformation equations or Translation and Rotation of Axes The coordinates (x', y') of a coordinate system with origin O' = (x_{0}, y_{0}) relative to the standard origin (0, 0) and with the x'axis making an angle of α with the positive xaxis are related to the standard (x, y) coordinates by the transformation equations or #14 20060807 07:25:07
Re: Coordinate Geometry FormulasPolar Coordinates or Listing of Several Types of Polar Curves Use the Polar Grapher to graph these curves. Circle The equation for a circle of radius r_{0} centered at the origin is given by If the circle is centered at (c, α) and has radius r_{0}, its equation is Ellipse The equation of an ellipse of semimajor axis a and semiminor axis b centered at the origin is given by Parabola If the distance from the vertex to the focus of a parabola is a, then its equation is Hyperbola The equation of a hyperbola of semimajor axis a and semiminor axis b centered at the origin is given by Lemniscate The equation of a lemniscate in polar coordinates is In rectangular coordinates this is The area inside both loops of the lemniscate is Cardioid The equation of a cardioid is given by The area of the cardioid is and its perimeter is ThreeLeaved Rose The equation of a threeleaved rose is For odd n, r = a cos nθ and r = a sin nθ are nleaved roses. FourLeaved Rose The equation of a fourleaved rose is For even n, r = a cos nθ and r = a sin nθ are 2nleaved roses. Limaçon The equation of a limaçon is Spiral of Archimedes The equation of a spiral of Archimedes is Last edited by Zhylliolom (20060807 08:06:23) #15 20070812 21:14:40
Re: Coordinate Geometry FormulasTurning point of a parabola of the form y=ax² +bx+c Last edited by Identity (20070812 21:15:59) 