## Mathematical Topics:

 Analytic Geometry 2 Subject 1: The ellipse: definition, foci, equation, tangent, intersection with a line. Level 1 : Axes and foci of the ellipse x²/a² + y²/b² = 1 Level 2 : Equation of the ellipse given a and c Level 3 : Equation of the tangent line Level 4 : Intersection points of an ellipse and a line Level 5 : Ratio of distances to a point and a line Subject 2: The hyperbola: definition, foci, equation, asymptotes, tangent, intersection with a line. Level 1 : Axes, foci and asymptotes of the hyperbola x²/a² - y²/b² = 1 Level 2 : Equation of the hyperbola given a and c Level 3 : Equation of the tangent line Level 4 : Intersection points of a hyperbola and a line Level 5 : Ratio of distances to a point and a line Subject 3: The parabola: definition, focus, directrix, parameter, equation, tangent, intersection with a line, tangents from an external point. Level 1 : Find the parameter, the focus and the directrix Level 2 : Find the parabola equation given certain data (e.g. the focus) Level 3 : Find the tangent to the parabola at a given point Level 4 : The intersection points of a parabola and a line Level 5 : Find the tangent passing through an external point

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