Question

Use the below figure for the following:

• In the upper portion of the circle, at the centre X, draw angles of 20°, V₁ X K₁ and V₂ X K₂; K₁ and K₂ being the points on the circle. Draw an ellipse joining K₁ and K₂.
• In the lower half of the circle, mark angles of 60° and name the points on the circle as P₁ and P₂.
• Draw an ellipse joining P₁ and P₂.

Can you tell?

• Are the distances between K₁ K₂ and P₁ P₂ the same?
• Compare the distances XK₁ and XP₂. Are these distances the same or are they different?
• Now compare the ellipses you have drawn.
• Which is the larger ellipse? Why?

Answer 1

• No, the distance between K₁ K₂ and P₁ P₂ are not the same.
• No, the distances are the same.
• The ellipse joining P₁P₂ is larger than the ellipse joining K₁K₂.
• The ellipse joining P₁P₂ is larger because:
  • The points P₁ and P₂ are farther apart than K₁ and K₂ due to the larger subtended angles (60° vs. 20°).
  • This greater distance increases the size of the ellipse, making it wider and larger.