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