Two ellipses are given below:
E₁: 169x2+49y2=1, E₂: 64x2+100y2=1
Answer the following questions.
(i) For each ellipse, identify the lengths of the semi-major axis and the semi-minor axis, and state whether its major axis is parallel to the x-axis or the y-axis.
(ii) Without plotting the curves, give a reasoned argument to decide which ellipse appears “flatter”, that is, farther from being a circle.
(iii) Calculate the eccentricity of each ellipse and verify the conclusion reached in part (ii).
(iv) Compare the distances between the two foci in E₁ and E₂. Explain how this comparison is consistent with your answer in part (ii).