Conic Sections And Circles

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| By Jhoanne Perez

Jhoanne Perez

Community Contributor

Quizzes Created: 1 | Total Attempts: 74

Questions: 10 | Attempts: 74 | Updated: Mar 3, 2023

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Questions and Answers

1.

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
B. Center (0, 0) , radius = 6

Explanation
The correct answer is Center (0, 0) , radius = 6. This is because the graph is centered at the point (0, 0) and the distance from the center to any point on the graph is 6 units.

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2.

What is the equation of the circle whose center is (-6,-15) and 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 correct answer is Option 2.

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3.

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

This is a set of all coplanar points such that 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 all coplanar points that are equidistant from a fixed point, known as the center. The distance from any point on the circle to the center remains constant, which defines the shape of a circle. This property distinguishes a circle from other conic sections such as the parabola, hyperbola, and ellipse, which have different characteristics and equations.

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5.

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

Explanation
The curve formed by the intersection of a plane and a double circular right cone is known as a conic. A conic is a general term that includes various types of curves such as circles, ellipses, parabolas, and hyperbolas. In this case, since the cone is double circular, the resulting curve would be a conic. Therefore, the correct answer is conic.

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6.

Given the radius is 8 and the center is at the origin, find the equation of the circle.
- A.
  
  X² +y² =64
- B.
  
  X² +y² =8
- C.
  
  X² -y² =64
- D.
  
  X² - y² =8
Correct Answer
A. X² +y² =64

Explanation
The equation of a circle with radius r and center at the origin (0,0) is given by x^2 + y^2 = r^2. In this case, the radius is 8, so the equation of the circle is x^2 + y^2 = 64.

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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 a quadratic equation is given by Ax^2 + By^2 + Cx + Dy + E = 0, where A, B, C, D, and E are constants. In the given equation x^2 + y^2 + 14x - 12y + 4 = 0, we can rearrange the terms to match the standard form. By grouping the x-terms and the y-terms separately, we get (x^2 + 14x) + (y^2 - 12y) + 4 = 0. Completing the square for both x and y, we have (x^2 + 14x + 49) + (y^2 - 12y + 36) + 4 - 49 - 36 = 0. Simplifying further, we get (x + 7)^2 + (y - 6)^2 - 81 = 0. Therefore, the standard form of the equation is (x + 7)^2 + (y - 6)^2 = 81, which matches with Option 1.

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8.

What is the equation of the circle given that the center is (3, -2) and a 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 given by (x-h)^2 + (y-k)^2 = r^2. In this case, the center is (3, -2) and the radius is 4. Plugging these values into the equation, we get (x-3)^2 + (y+2)^2 = 16, which is the equation of the circle.

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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 match the given center (-3, 13) and the radius value is also 4, which matches the given radius value.

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Current Version
Mar 03, 2023

Quiz Edited by
ProProfs Editorial Team
Sep 11, 2020

Quiz Created by
Jhoanne Perez

Conic Sections And Circles

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 radius is square root of 5

What is the equation of the circle given this graph?

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

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

Given the radius is 8 and the center is at the origin, 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 a 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