A Mathematical Exam About Ellipse & Hyperbola. Be A Mathematician
A hyperbola is an open curve with two branches, the intersection of a plane with both halves of a double cone. The plane does not have to be parallel to the axis of the cone; the hyperbola will be symmetrical in any case.
In mathematics, an ellipse is a plane curve surrounding two focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant.
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- 1.
It is the set of points in plane such that the difference of its distances from two fixed points is constant
- A.
Circle
- B.
Parabola
- C.
Ellipse
- D.
Hyperbola
Correct Answer
D. HyperbolaExplanation
A hyperbola is defined as the set of points in a plane such that the difference of its distances from two fixed points (called the foci) is constant. This means that for any point on the hyperbola, the difference between its distance to one focus and its distance to the other focus is always the same. This property distinguishes a hyperbola from other conic sections like a circle, parabola, or ellipse, which have different distance properties. Therefore, the given description aligns with the definition of a hyperbola.Rate this question:
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- 2.
A segment passing through the focus of the ellipse/hyperbola that is perpendicular to the major axis.
- A.
Asymptote
- B.
Directix
- C.
Latus rectum
- D.
Transverse axis
Correct Answer
C. Latus rectumExplanation
The latus rectum is a segment passing through the focus of the ellipse/hyperbola that is perpendicular to the major axis. It is a key property of conic sections and is used to define the shape and dimensions of the ellipse or hyperbola. The latus rectum plays an important role in determining the focal length and eccentricity of the conic section.Rate this question:
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- 3.
The segment made by the endpoints of the vertices of a hyperbola is called
- A.
Conjugate axis
- B.
Major axis
- C.
Minor axis
- D.
Transverse axis
Correct Answer
D. Transverse axisExplanation
The segment made by the endpoints of the vertices of a hyperbola is called the transverse axis. This axis is the line segment that passes through the center of the hyperbola and is perpendicular to the conjugate axis. It is the longest segment in the hyperbola and determines the overall shape and orientation of the hyperbola.Rate this question:
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- 4.
Is [e = .98 an ellipse] true or false?
- A.
True
- B.
False
Correct Answer
A. TrueExplanation
The statement "e = .98 an ellipse" is true. In mathematics, e represents the eccentricity of an ellipse. An ellipse is a closed curve that resembles a flattened circle, and its eccentricity value must be between 0 and 1. Therefore, if e = .98, it falls within the valid range and satisfies the definition of an ellipse.Rate this question:
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- 5.
Is [Ellipse the best structure to follow in making a Cooling Tower in powerplant because of its efficiency in heat removing process ?] true or false?
- A.
True
- B.
False
Correct Answer
B. FalseExplanation
The statement suggests that an ellipse is the best structure to follow in making a cooling tower in a power plant because of its efficiency in the heat removing process. However, this statement is false. The efficiency of a cooling tower in the heat removing process is not determined by its shape, such as an ellipse. The efficiency of a cooling tower depends on various factors such as the design, size, materials used, and the specific cooling requirements of the power plant. Therefore, it is incorrect to claim that an ellipse is the best structure for a cooling tower in a power plant.Rate this question:
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- 6.
The standard equation 9x2 - 4y2 = 36 is
- A.
Option 1
- B.
Option 2
- C.
Option 3
- D.
Option 4
Correct Answer
A. Option 1Explanation
The standard equation 9x^2 - 4y^2 = 36 represents a hyperbola. The coefficients of x^2 and y^2 are positive and different, indicating that the hyperbola opens horizontally. The equation is in the standard form of a hyperbola, where the squares of x and y are divided by positive constants and subtracted to equal a constant. Therefore, the correct answer is Option 1.Rate this question:
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- 7.
What
- A.
Option 1
- B.
Option 2
- C.
Option 3
- D.
Option 4
Correct Answer
A. Option 1 -
- 8.
What is area of an ellipse?
Correct Answer
π ABExplanation
The area of an ellipse is given by the formula πAB, where A and B are the lengths of the semi-major and semi-minor axes of the ellipse, respectively. This formula is derived from the mathematical definition of an ellipse and is used to calculate its area.Rate this question:
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