Conic Sections And Circles
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What is the equation of the circle whose center is (-6,-15) and radius is square root of 5
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Option 1
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Option 2
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Option 3
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Option 4
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Explore the fundamentals of geometry with our 'Conic Sections and Circles' quiz. Test your knowledge on circle equations, centers, radii, and the properties of conics. Ideal for students seeking to enhance their understanding of geometric principles.
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- 2.
What is the equation of the circle given that the center is (3, -2) and a radius is 4.
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Option 1
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Option 2
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Option 3
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Option 4
Correct Answer
A. Option 1Explanation
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.Rate this question:
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- 3.
Given the radius is 8 and the center is at the origin, find the equation of the circle.
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X2 +y2 =64
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X2 +y2 =8
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X2 -y2 =64
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X2 - y2 =8
Correct Answer
A. X2 +y2 =64Explanation
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.Rate this question:
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- 4.
Which of the following is the equation of the graph below?
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Option 1
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Option 2
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Option 3
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Option 4
Correct Answer
A. Option 4 -
- 5.
What is the equation of the circle given this graph?
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Option 1
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Option 2
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Option 3
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Option 4
Correct Answer
A. Option 1 -
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This is a set of all coplanar points such that the distance from a fixed point is constant.
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Circle
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Parabola
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Hyperbola
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Ellipse
Correct Answer
A. CircleExplanation
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.Rate this question:
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- 7.
What is the standard form of the equation x2 + y2 +14x -12y +4 = 0
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Option 1
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Option 2
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Option 3
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Option 4
Correct Answer
A. Option 1Explanation
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.Rate this question:
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- 8.
Which of the following is the center and the radius of this equation
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Center (-3, 13) radius=4
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Center (3, 13) radius=4
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Center (-3, -13) radius=4
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Center (3, -13) radius=4
Correct Answer
A. Center (3, 13) radius=4Explanation
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.Rate this question:
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- 9.
Which of the following is the center and the radius of the graph below
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Center (0, 0) , radius = 3
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Center (0, 0) , radius = 6
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Center (0, 0) , radius = 12
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Center (0, 0) , radius = 36
Correct Answer
A. Center (0, 0) , radius = 6Explanation
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.Rate this question:
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- 10.
This is a curve formed by the intersection of a plane and a double circular right cone
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Circle
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Conic
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Parabola
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Generator of the cone
Correct Answer
A. ConicExplanation
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.Rate this question:
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Current Version
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Dec 27, 2024Quiz Edited by
ProProfs Editorial Team -
Sep 11, 2020Quiz Created by
Jhoanne Perez