Questions with detailed step by step solutions from Coordinate Geometry

Topics covered under Coordinate Geometry
Cartesian system of rectangular co-ordinates in a plane, distance formula, section formula, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes. Straight lines Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line, equations of internal and external bisectors of angles between two lines, coordinates of centroid, orthocentre and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines. Circles, conic sections Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle when the end points of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to a circle, equation of the tangent. Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point (s) of tangency.
Distance Between Two Points in 2D
Various Forms of Equation of Line
Position of Points Relative to a Line
Distance of Point from a Line
Concurrent and Family of Lines
Angular Bisectors of Intersecting Lines
Image of a Point about a Line Mirror
Equation of Line in Parametric Form
Pair of Straight Lines Through Origin
General Equation of Pair of Straight Lines
Equation of Circles in Different Forms
Reflection Property of Ellipse
Position of a Point/Line w.r.t Circle
Non-intersecting, Intersecting, Touching circles
Position of Point w.r.t Parabola
Reflection Property of Parabola
Parabola of Form (ax+by)^2+2gx+2fy+c=0
Position of a Point w.r.t Ellipse
Equation of Ellipse in General Form
Position of a Point w.r.t Hyperbola
Concyclic Points of Hyperbola
Reflection Property of Hyperbola
Equation of Hyperbola in General Form