Conic Sections And Circle

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Joan Perez
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This is an assessment if you really understood the lesson about Conic sections and Circles

• 1.

• 2.

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

A. Circle
Explanation
A circle is defined as a set of all coplanar points that are equidistant from a fixed point called the center. The distance from any point on the circle to the center remains constant, which is the radius of the circle. Therefore, the given description perfectly matches the characteristics of a circle.

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• 3.

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

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 can take various forms depending on the angle at which the plane intersects the cone. It can be a circle, an ellipse, a parabola, or a hyperbola. Therefore, the correct answer is conic.

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• 4.

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

• A.

X + y2 =10

• B.

X + y2 =25

• C.

X - y2 =10

• D.

X - y2 =25

B. X + y2 =25
Explanation
The equation of a circle with center (0,0) and radius 5 is x^2 + y^2 = 25. This is because the equation of a circle with center (h,k) and radius r is (x-h)^2 + (y-k)^2 = r^2. In this case, h=0, k=0, and r=5, so plugging in these values gives us x^2 + y^2 = 25.

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• 5.

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

C. Option 3
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. So the equation of the circle is (x-3)^2 + (y+2)^2 = 4^2.

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• 6.

What is the equation of the circle whose Center is (−6, −15) and radius: square root of 5

• A.

Option 1

• B.

Option 2

• C.

Option 3

• D.

Option 4

• E.

Option 5

D. Option 4
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 (-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 4.

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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

C. Option 3
Explanation
The standard form of the equation x^2 + y^2 + 14x - 12y + 4 = 0 is obtained by rearranging the terms to have the x term and y term separately on one side of the equation and the constant term on the other side. This can be done by completing the square for both the x and y terms. The equation can then be written as (x + 7)^2 - 49 + (y - 6)^2 - 36 + 4 = 0, which simplifies to (x + 7)^2 + (y - 6)^2 = 81. Therefore, the correct answer is Option 3.

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• 8.

• A.

Option 1

• B.

Option 2

• C.

Option 3

• D.

Option 4

D. Option 4
• 9.

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

• A.

• B.

Center (0,0) radius =6

• C.

Center (0,0), radius= 12

• D.

Center (0,0), radius = 36

B. Center (0,0) radius =6
Explanation
The correct answer is center (0,0) radius =6. This means that the center of the graph is at the point (0,0) and the radius of the graph is 6 units. This implies that the graph is a circle with its center at the origin (0,0) and a radius of 6 units.

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• 10.

• A.

Option 1

• B.

Option 2

• C.

Option 3

• D.

Option 4

D. Option 4
• 11.

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

B. Center (3,13)   radius= 4
Explanation
The correct answer is center (3,13) & radius= 4. This is because the center of a circle is represented by the coordinates (h, k), where h is the x-coordinate and k is the y-coordinate. In this case, the center is (3,13), indicating that the circle is centered at the point (3,13) on the coordinate plane. The radius of a circle is the distance from the center to any point on the circle. Given that the radius is 4, it means that the distance from the center to any point on the circle is 4 units.

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