Coordinate Geometry 2

This advanced geometry topic focuses on conic sections (circle, parabola, ellipse, and hyperbola) in the coordinate plane. Learners analyse these curves algebraically and geometrically, applying their properties in solving complex spatial problems.

Learning Outcomes:
The learner should be able to:

• Determine the equation of the locus of a variable point.
• Determine the equation of a circle.
• Determine the tangent to a circle and its relationship to the radius.
• Determine length of tangent drawn from a point outside the circle.
• Use concepts of perpendicular lines or differentiation to determine the tangent to a circle at a point.
• Deduce the conditions for external, internal and orthogonal intersection of circles.
• Define and sketch a parabola.
• Identify its vertex and line of symmetry, locate its focus and directrix.
• Determine the equation of the parabola.
• Determine the equation of the tangent, normal and chord of a parabola.
• Determine the parametric equations of the parabola.
• Sketch and identify an ellipse.
• Identify the major and minor axis and semis axis and their lengths.
• Find the eccentricity, foci, and equations of directrices.
• Find the parametric equations of the ellipse.
• Find the equation of the tangent, normal and chord of an ellipse.
• Analyse locus of parabola and ellipse to solve contextual problems in geometry, motion, engineering and architecture.