Free Test Conic Sections (Parabo... – JEE

Q1: The standard equation of a parabola with vertex at origin and axis along the x-axis is:

A. y^2 = 4ax B. x^2 = 4ay C. y^2 = 4ay D. x^2 = 4ax

Q2: Which of the following is the eccentricity of a circle?

A. 0 B. 1 C. ∞ D. 2

Q3: What is the eccentricity of a parabola?

A. 0 B. 1 C. Greater than 1 D. Less than 1

Q4: The equation x^2 + y^2 + 2gx + 2fy + c = 0 represents a circle if:

A. g = 0 B. f = 0 C. c = 0 D. g^2 + f^2 > c

Q5: In the equation of an ellipse x^2/a^2 + y^2/b^2 = 1, if a > b, then the major axis is:

A. Along x-axis B. Along y-axis C. Both axes D. Can’t say

Q6: What is the standard equation of a hyperbola with transverse axis along x-axis?

A. x^2/a^2 - y^2/b^2 = 1 B. x^2/a^2 + y^2/b^2 = 1 C. y^2/a^2 - x^2/b^2 = 1 D. x^2 + y^2 = r^2

Q7: Which conic section is defined as the set of all points where the distance from a fixed point and a fixed line is equal?

A. Circle B. Parabola C. Ellipse D. Hyperbola

Q8: What is the latus rectum of the parabola y^2 = 4ax?

A. 2a B. 4a C. a D. 8a

Q9: For an ellipse, the sum of the distances from any point on the ellipse to the two foci is:

A. Equal to major axis B. Equal to minor axis C. Equal to 2a D. Equal to 2b

Q10: The asymptotes of a hyperbola are:

A. The axes B. The diagonals C. Lines that the curve approaches D. Tangents

Q11: The number of directrices in an ellipse is:

A. 1 B. 2 C. 3 D. 4

Q12: The foci of a hyperbola lie:

A. Inside the ellipse B. On the same side C. On opposite sides of the center D. At the origin

Q13: Which of the following conics does not have asymptotes?

A. Hyperbola B. Ellipse C. Parabola D. Circle

Q14: What is the length of the latus rectum of an ellipse?

A. 2a B. 2b C. 2b^2/a D. 2a^2/b

Q15: Which of the following represents an ellipse?

A. x^2 - y^2 = 1 B. x^2 + y^2 = 1 C. x^2/a^2 + y^2/b^2 = 1 D. Both B and C

Q16: In an ellipse, if e is the eccentricity, then:

A. e < 1 B. e = 1 C. e > 1 D. e = 0

Q17: Which conic has the property that the difference of distances from any point to two fixed points is constant?

A. Parabola B. Circle C. Ellipse D. Hyperbola

Q18: In the parabola y^2 = 4ax, the focus is located at:

A. (a, 0) B. (0, a) C. (a, a) D. (0, 0)

Q19: Which of these represents the condition for a conic to be an ellipse?

A. e = 1 B. e < 1 C. e > 1 D. e = 0

Q20: Which of these conics has only one focus and one directrix?

A. Circle B. Ellipse C. Parabola D. Hyperbola

Quiz for Conic Sections (Parabola, Ellipse, Hyperbola)