by swilderman
Dive into the intriguing realm of conic sections, where geometry and algebra intersect to form beautiful curves and shapes. This quiz will test your understanding of circles, ellipses, parabolas, and hyperbolas, challenging your knowledge of their unique properties and equations. Sharpen your pencils and get ready to explore the elegance of conic sections. Good luck!
We recommend that you do not leave the page that you are taking this quiz in. Stay honest 🙂
Conic Sections Quiz Questions Overview
1. Which of the following is the general equation of a circle?
Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0
(x – h)^2 + (y – k)^2 = r^2
Ax^2 + Cy^2 + Dx + Ey + F = 0
y = ax^2 + bx + c
2. What is the eccentricity of a circle?
0
1
Greater than 1
Between 0 and 1
3. Which conic section is represented by the equation y^2 = 4ax?
Circle
Ellipse
Parabola
Hyperbola
4. In the standard form of an ellipse, (x^2/a^2) + (y^2/b^2) = 1, what do ‘a’ and ‘b’ represent?
Foci
Vertices
Semi-major and semi-minor axes
Directrices
5. What is the eccentricity of a hyperbola?
0
1
Greater than 1
Between 0 and 1
6. Which conic section has two branches?
Circle
Ellipse
Parabola
Hyperbola
7. What is the directrix of a parabola?
A fixed point
A fixed line
The vertex
The axis of symmetry
8. Which conic section can be formed by slicing a cone parallel to its base?
Circle
Ellipse
Parabola
Hyperbola
9. In the equation of a hyperbola, (x^2/a^2) – (y^2/b^2) = 1, what do ‘a’ and ‘b’ represent?
Foci
Vertices
Semi-major and semi-minor axes
Asymptotes
10. Which conic section is defined as the set of all points where the sum of the distances to two fixed points (foci) is constant?
Circle
Ellipse
Parabola
Hyperbola
11. What is the equation of a parabola with vertex at the origin and focus at (0, p)?
x^2 = 4py
y^2 = 4px
x^2 + y^2 = r^2
x^2 – y^2 = 1
12. Which conic section can be formed by slicing a cone perpendicular to its base?
Circle
Ellipse
Parabola
Hyperbola
13. In the standard form of a hyperbola, (x^2/a^2) – (y^2/b^2) = 1, what is the relationship between ‘a’ and ‘b’?
a > b
a < b
a = b
a and b are unrelated
14. What is the standard form of the equation of a hyperbola with a vertical transverse axis?
(x^2/a^2) – (y^2/b^2) = 1
(y^2/a^2) – (x^2/b^2) = 1
(x^2/a^2) + (y^2/b^2) = 1
(y^2/a^2) + (x^2/b^2) = 1
15. Which conic section is represented by the equation (x^2/a^2) + (y^2/b^2) = 1?
Circle
Ellipse
Parabola
Hyperbola
16. What is the focus of a parabola with the equation y^2 = 4ax?
(a, 0)
(0, a)
(0, 4a)
(a, 4a)
17. Which conic section has an eccentricity of 1?
Circle
Ellipse
Parabola
Hyperbola
18. What is the standard form of the equation of a parabola with a horizontal axis of symmetry?
y^2 = 4ax
x^2 = 4ay
y = ax^2 + bx + c
x = ay^2 + by + c
We recommend that you do not leave the page that you are taking this quiz in. Stay honest 🙂
