1.
What is the equation of the given circle based on the graph?
Correct Answer
D. Option 4
2.
Which of the following is the center and the radius of the graph below?
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.
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.
4.
This is a set of coplanar points such as the distance from a fixed point is constant.
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.
5.
This is a curve formed by the intersection of a plane and a double right circular 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.
6.
Given the center at (0,0) and the radius is 5, find the equation of the circle.
Correct Answer
B. X^{2} + y^{2 }= 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.
7.
What is the standard form of the equation x^{2} + y^{2} +14x -12y+4=0
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.
8.
What is the equation of the circle given that the center is (3, -2) and radius is 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.
9.
Which of the following is the equation of the graph below?
Correct Answer
D. Option 4
10.
Which of the following is the center and the radius of this equation
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.