Splendid Math Conic Sections Test - 70+ MCQs: Math Conic Sections Quiz: Explore the World of Conic Curves with Challenging Questions

1. What is the eccentricity of a circle?

Undefined

2. What is the standard form equation of a parabola in the Cartesian coordinate system?

(x - h)² = 4a(y - k)

y = mx + b

y² = 4ax

x² + y² = r²

3. Define the semi-latus rectum of a parabola.

Length of the latus rectum

Distance between the focus and the directrix

Half the length of the latus rectum

Double the length of the latus rectum

4. Define the directrix of a hyperbola.

Midpoint of the latus rectum

Line parallel to the major axis

Line equidistant from the foci

Intersection of axes

5. What is the relationship between the focal length 'f' and the radius of curvature 'R' for a parabola?

f = R

f = 2R

f = 3R

f = 4R

6. In the equation y² = 4ax, what type of conic section is represented?

Circle

Ellipse

Parabola

Hyperbola

7. Define the focus of an ellipse.

Midpoint of the latus rectum

Point equidistant from the directrix

Intersection of axes

Point equidistant from the endpoints of the major axis

8. What is the relationship between the focal length 'f' and the semi-major axis 'a' for an ellipse?

f = a

f = 2a

f = 3a

f = 4a

9. For a parabola, what is the relationship between the focus and the directrix?

Equal

Focus is twice as far from the directrix

No specific relationship

Directrix is twice as far from the focus

10. Define the focus-directrix property of a parabola.

Directrix is a mirror image of the focus

Focus is equidistant from the directrix and vertex

Directrix is perpendicular to the axis of symmetry

Focus is twice as far from the directrix as the directrix is from the vertex

Math Conic Sections MCQ Test 5