Welcome to Class 11 Maths MCQ – Conic Sections chapter. Here are 20 multiple-choice questions to sharpen your knowledge of conic sections in Maths.
1. Which of the following is defined by the equation x^2 + y^2 = r^2?
Answer:
Explanation:
A circle is defined by the set of all points equidistant (distance r) from a fixed point (the center).
2. Which conic section is represented by the equation x^2/a^2 – y^2/b^2 = 1?
Answer:
Explanation:
A hyperbola is defined by the difference of distances from two fixed points (foci).
3. The equation y^2 = 4ax represents:
Answer:
Explanation:
This is the standard form of a parabola that opens upwards.
4. For an ellipse, if a = b, the shape becomes a:
Answer:
Explanation:
When the major and minor axes are equal, the ellipse becomes a circle.
5. The latus rectum of the parabola y^2 = 4ax is:
Answer:
Explanation:
The latus rectum of this parabola is the length 2a.
6. The eccentricity of a circle is:
Answer:
Explanation:
A circle's eccentricity is zero because the distance from any point on the circle to the center is constant.
7. The equation representing a horizontal ellipse is:
Answer:
Explanation:
For a horizontal ellipse, the major axis is along the x-axis.
8. The standard equation of an ellipse with its center at the origin and major axis along y-axis is:
Answer:
Explanation:
For an ellipse with major axis along the y-axis, the value of 'a' is greater and along y-axis.
9. If e is the eccentricity of an ellipse, then:
Answer:
Explanation:
The eccentricity of an ellipse is always between 0 and 1.
10. A parabola has:
Answer:
Explanation:
A parabola is defined by one focus and one directrix.
11. The distance between the foci of the ellipse x^2/9 + y^2/4 = 1 is:
Answer:
Explanation:
The distance between the foci is 2c, where c^2 = a^2 – b^2. Using the given equation, c = √5, so the distance is 2√5.
12. The eccentricity of a hyperbola is:
Answer:
Explanation:
The eccentricity of a hyperbola is always greater than 1.
13. The foci of the hyperbola x^2/9 – y^2/4 = 1 are located on:
Answer:
Explanation:
The foci of the hyperbola with a horizontal transverse axis are located on the x-axis.
14. The directrices of the ellipse x^2/4 + y^2/9 = 1 are:
Answer:
Explanation:
The equation of directrices for an ellipse with horizontal major axis is x = ±a/e.
15. For which conic section is the eccentricity undefined?
Answer:
Explanation:
The eccentricity of a parabola is not defined.
16. The latus rectum of the ellipse x^2/25 + y^2/16 = 1 is:
Answer:
Explanation:
The latus rectum of an ellipse is 2b^2/a.
17. Which of the following conic sections does not have a directrix?
Answer:
Explanation:
A circle does not have a directrix.
18. If a hyperbola has its transverse axis along the y-axis, its equation is of the form:
Answer:
Explanation:
For a hyperbola with its transverse axis along the y-axis, the positive term is associated with y^2.
19. The vertices of the ellipse x^2/16 + y^2/9 = 1 lie on:
Answer:
Explanation:
The ellipse has its major axis along the x-axis, so its vertices lie on the x-axis.
20. Which of the following is not a conic section?
Answer:
Explanation:
Polynomial is not a conic section; it's a type of mathematical expression.