Goals and Objectives of the
Ellipse Module

After completing this module you will be able to: describe that a circle is a special ellipse. describe that the equation Ax2 +By2 = P represents an ellipse when the coefficients A, B and P are the same sign. describe that the equation Ax2 +By2 = P represents an ellipse that is not a circle when the coefficients A and B are not equal, but have the same sign. describe that the equation Ax2 +By2 = P represents an ellipse that is a circle when the coefficients A and B are the same. describe that an ellipse has two axes of symmetry. describe the axis of symmetry parallel to the x-axis as the horizontal axis of an ellipse. describe the axis of symmetry parallel to the y-axis as the vertical axis of an ellipse. write the standard equation of an ellipse centred at the origin as x2/ a2 + y2/ b2 = 1. write the standard equation for an ellipse centred at any point (h, k) as (x - h)2/ a2 + (y - k)2/ b2 = 1. describe what the variables h, k, a and b represent in the standard equation of an ellipse. describe the effect that varying a and b in the standard equation has on the ellipse. write the standard equation of an ellipse using its centre coordinates and the lengths of its horizontal and vertical axes. rewrite an equation of an ellipse from standard form to an equation of the form Ax2 + By2 + Cx + Dy + F = 0. rewrite an equation of the form Ax2 + By2 + Cx + Dy + F = 0 into the standard form (x - h)2/ a2 + (y - k)2/ b2 = 1. show that the standard equation of an ellipse is equal to the general ellipse equation of the form Ax2 + By2 + Cx + Dy + F = 0. describe that the coefficients of x2 and y2 must be the same sign in the general equation Ax2 + By2 + Cx + Dy + F = 0 in order for an ellipse to exist. describe that an ellipse that is not a circle is defined by the equation Ax2 + By2 + Cx + Dy + F = 0 when the coefficients of x2 and y2 are different. describe that a special ellipse called a circle is defined by the equation Ax2 + By2 + Cx + Dy + F = 0 when the coefficients of x2 and y2 are the same. describe what happens when a plane cuts the double-napped cone at various angles and heights along the vertical axis of the cone.