Conic Sections And Introduction To Circles

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| By Joan Perez

Joan Perez

Community Contributor

Quizzes Created: 1 | Total Attempts: 64

Questions: 10 | Attempts: 64 | Updated: Mar 3, 2023

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Questions and Answers

1.

What is the equation of the given circle based on the graph?
- A.
  
  Option 1
- B.
  
  Option 2
- C.
  
  Option 3
- D.
  
  Option 4
Correct Answer
D. Option 4
2.

Which of the following is the center and the radius of the graph below?
- A.
  
  Center (0,0) radius= 3
- B.
  
  Center (0,0) radius= 6
- C.
  
  Center (0,0) radius= 12
- D.
  
  Center (0,0) radius= 36
Correct Answer
D. Center (0,0) radius= 36
3.

What is the equation of the circle whose center is (-6,-15) and a radius is square root of 5.
- A.
  
  Option 1
- B.
  
  Option 2
- C.
  
  Option 3
- D.
  
  Option 4
Correct Answer
B. Option 2

Explanation
The equation of a circle with center (h,k) and radius r is given by (x-h)^2 + (y-k)^2 = r^2. In this case, the center is (-6,-15) and the radius is the square root of 5. Plugging these values into the equation, we get (x+6)^2 + (y+15)^2 = 5. Therefore, the equation of the circle is (x+6)^2 + (y+15)^2 = 5.

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4.

This is a set of coplanar points such as the distance from a fixed point is constant.
- A.
  
  Circle
- B.
  
  Parabola
- C.
  
  Hyperbola
- D.
  
  Ellipse
Correct Answer
A. Circle

Explanation
A circle is a set of coplanar points where the distance from a fixed point (called the center) is constant. The distance between any point on the circle and the center is always the same, which makes it a perfect fit for the given description.

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5.

This is a curve formed by the intersection of a plane and a double right circular cone
- A.
  
  Circle
- B.
  
  Conic
- C.
  
  Parabola
- D.
  
  Generator of the cone
Correct Answer
B. Conic

Explanation
The given statement describes a curve formed by the intersection of a plane and a double right circular cone. This curve is known as a conic. A conic is a type of curve that includes circles, ellipses, parabolas, and hyperbolas. Since the question asks for the correct answer, the term "conic" accurately represents the curve formed by the intersection of the plane and the double right circular cone.

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6.

Given the center at (0,0) and the radius is 5, find the equation of the circle.
- A.
  
  X² + y²= 10
- B.
  
  X² + y²= 25
- C.
  
  X² - y²= 10
- D.
  
  X² - y²= 25
Correct Answer
B. X² + y²= 25

Explanation
The equation of a circle with center (0,0) and radius 5 is x^2 + y^2 = 25. This equation represents all the points (x,y) that are 5 units away from the center (0,0), forming a circle with a radius of 5.

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7.

What is the standard form of the equation x² + y² +14x -12y+4=0
- A.
  
  Option 1
- B.
  
  Option 2
- C.
  
  Option 3
- D.
  
  Option 4
Correct Answer
A. Option 1

Explanation
The standard form of the equation x2 + y2 + 14x - 12y + 4 = 0 is (x + 7)2 + (y - 6)2 = 25. This is because the standard form of the equation of a circle is (x - h)2 + (y - k)2 = r2, where (h, k) is the center of the circle and r is the radius. In this case, the center of the circle is (-7, 6) and the radius is 5.

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8.

What is the equation of the circle given that the center is (3, -2) and radius is 4.
- A.
  
  Option 1
- B.
  
  Option 2
- C.
  
  Option 3
- D.
  
  Option 4
Correct Answer
A. Option 1

Explanation
The equation of a circle with center (h, k) and radius r is (x-h)^2 + (y-k)^2 = r^2. In this case, the center is (3, -2) and the radius is 4. Therefore, the equation of the circle is (x-3)^2 + (y+2)^2 = 16.

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9.

Which of the following is the equation of the graph below?
- A.
  
  Option 1
- B.
  
  Option 2
- C.
  
  Option 3
- D.
  
  Option 4
Correct Answer
D. Option 4
10.

Which of the following is the center and the radius of this equation
- A.
  
  Center (-3, 13) radius= 4
- B.
  
  Center (3, 13) radius= 4
- C.
  
  Center (-3, -13) radius= 4
- D.
  
  Center (3, -13) radius= 4
Correct Answer
B. Center (3, 13) radius= 4

Explanation
The correct answer is center (3, 13) radius= 4. This is because the center coordinates (-3, 13) and (3, 13) are the only ones that have the same y-coordinate, which matches the given equation. Additionally, the radius of 4 matches the given equation.

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Current Version
Mar 03, 2023

Quiz Edited by
ProProfs Editorial Team
Sep 06, 2020

Quiz Created by
Joan Perez

Conic Sections And Introduction To Circles

What is the equation of the given circle based on the graph?

Which of the following is the center and the radius of the graph below?

What is the equation of the circle whose center is (-6,-15) and a radius is square root of 5.

This is a set of coplanar points such as the distance from a fixed point is constant.

This is a curve formed by the intersection of a plane and a double right circular cone

Given the center at (0,0) and the radius is 5, find the equation of the circle.

What is the standard form of the equation x2 + y2 +14x -12y+4=0

What is the equation of the circle given that the center is (3, -2) and radius is 4.

Which of the following is the equation of the graph below?

Which of the following is the center and the radius of this equation

What is the standard form of the equation x² + y² +14x -12y+4=0