1A plane cuts a cone parallel to its base. Which conic section is formed: parabola, ellipse, circle or hyperbola?
2A plane cuts a cone perpendicular to its axis without passing through the vertex. What is the conic section called: parabola, ellipse, circle or hyperbola?
3A plane cuts a right circular cone so that the angle it makes with the axis is less than the semi-vertical angle. What is the conic section called: parabola, ellipse, circle or hyperbola?
4A plane cuts a cone parallel to its generator. What is the conic section called: parabola, ellipse, circle or hyperbola?
5The semi-vertical angle of a cone is \( \alpha \) and a plane makes an angle \( \theta \) with the axis. If \( \alpha < \theta < 90^\circ \), which conic section is formed: parabola, ellipse, circle or hyperbola?
6The semi-vertical angle of a cone is \( \alpha \) and a plane makes an angle \( \theta \) with the axis. If \( \theta = \alpha \), which conic section is formed: parabola, ellipse, circle or hyperbola?
7The semi-vertical angle of a cone is \( \alpha \) and a plane makes an angle \( \theta \) with the axis. If \( \theta < \alpha \), which conic section is formed: parabola, ellipse, circle or hyperbola?
8Which of these is NOT a conic section: parabola, ellipse, circle or straight line?
9In a right circular cone ABC, A is the top point, B is the centre of the base and C is a point on the edge of the base. Name the point A, the line AB, the line AC, the angle BAC and the line BC.
10Name each shape: a perfectly round closed curve; a closed curve stretched in one direction; a single open U shaped curve; a curve made of two separate open branches facing away from each other.
11Define a circle as a conic section.
12Define an ellipse as a conic section.
13Define a parabola as a conic section.
14Define a hyperbola as a conic section.
15Under what condition is a circle formed?
16Under what condition is an ellipse formed?
17Under what condition is a parabola formed?
18Under what condition is a hyperbola formed?
19Why is the angle between the axis and a generator called the SEMI-vertical angle?
20Why does a hyperbola need a doubled mapped right circular cone while the other three curves do not?
21A cone has a semi-vertical angle of \( 25^\circ \). A plane cuts it at \( 70^\circ \) to the axis. Name the conic section and give the reason.
22Give one everyday object that shows each of the four conic sections.