Quiz on Ellipses

What is the shape formed when a plane intersects a cone parallel to the base?

• Hyperbola

• Parabola

• Ellipse

• Circle

How many foci does an ellipse have?

• Two

• Four

• One

• Three

What is the center of an ellipse?

• Vertex

• Midpoint of the line segment connecting the foci

• Focus

• Intersection point of major and minor axes

Which axis of symmetry is longer in an ellipse?

• Major axis

• Minor axis

• None of the above

• Both are equal

What is the standard form of the equation of an ellipse with its center at the origin?

• x^2 - y^2 = 1

• x^2/a^2 + y^2/b^2 = 1

• x^2 + y^2 = 1

• x^2/a^2 - y^2/b^2 = 1

What does the value of A represent in the equation of an ellipse?

• Distance from the center to a vertex on the major axis

• Distance from the center to a focus

• Distance from the center to the ellipse itself

• Distance from the center to a vertex on the minor axis

If an ellipse is wider than it is tall, which axis is the major axis?

• Vertical axis

• Horizontal axis

• Both are equal

• None of the above

How can an ellipse be transformed in terms of its equation?

• By changing the minor axis length

• By changing the foci

• By changing the major axis length

• By changing the center coordinates

What is the significance of ellipses in astronomy and astrophysics?

• They represent parabolic orbits of celestial objects

• They represent elliptical orbits of celestial objects

• They are not relevant in astronomy

• They represent circular orbits of celestial objects

How many foci does an ellipse have?

• One

• Two

• Three

• Four