Cone in three dimension

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According to me the following statements are true

Statement 1: The guiding curve of a right circular cone is always a circle.

Statement 2: If the guiding curve is a circle then the cone may or may not be right circular.

Am I right?

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You are right. Further, it is also true that a cone is right circular if and only if its guiding curve is a circle and its vertex lies on the normal to the base passing through the center of that circle.