Question

Which of the following is incorrect about Ellipse?

(a) Eccentricity is less than 1

(b) Mathematical equation is X^2 /a^2 + Y^2/b^2 = 1

(c) If a plane is parallel to axis of cone cuts the cone then the section gives ellipse

(d) The sum of the distances from two focuses and any point on the ellipse is constant

The question was posed to me in semester exam.

This question is from Construction of Ellipse in division Geometrical Construction of Engineering Drawing

Answer 1

The correct answer is (c) If a plane is parallel to axis of cone cuts the cone then the section gives ellipse

To explain I would say: If a plane is parallel to the axis of cone cuts the cone then the cross-section gives hyperbola. If the plane is parallel to base it gives circle. If the plane is inclined with an angle more than the external angle of cone it gives parabola. If the plane is inclined and cut every generators then it forms an ellipse.