1.
Which of the following is the center and the radius of this equation x^{2} +y^{2} -6x -26y +162 =0
Correct Answer
B. Center (3,13) radius =4
Explanation
The equation of a circle can be written in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) represents the center of the circle and r represents the radius. In this case, the equation x^2 + y^2 - 6x - 26y + 162 = 0 can be rearranged to (x - 3)^2 + (y - 13)^2 = 4^2. Therefore, the center of the circle is (3, 13) and the radius is 4.
2.
Which of the following is the equation of the graph below?
Correct Answer
D. Option 4
3.
What is the equation of the circle given that the center is (3,-2) and radius =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. Therefore, Option 1 is the correct answer.
4.
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 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, we can rewrite it as x^2 + y^2 + 14x - 12y + 4 = 0. By rearranging the terms, we can see that the equation is in the standard form with A = 1, B = 1, C = 14, D = -12, and E = 4. Therefore, the correct answer is Option 1.
5.
Given the center at (0,0) and the radius is 5, find the equation of the circle.
Correct Answer
C. 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 origin (0,0), forming a circle with a radius of 5.
6.
This is a curve formed by the intersection of a plane and a double right circular cone.
Correct Answer
B. Conic
Explanation
A conic is the correct answer because it is a curve formed by the intersection of a plane and a double right circular cone. A conic can take different forms depending on the angle and position of the intersecting plane, such as a circle, ellipse, parabola, or hyperbola. In this case, the intersecting plane forms a conic shape, but without further information, we cannot specify which specific type of conic it is.
7.
This is a set of all coplanar points such that the distance from a fixed point is constant.
Correct Answer
A. Circle
Explanation
A circle is defined as a set of all coplanar points that are equidistant from a fixed point called the center. This means that the distance from any point on the circle to the center is constant. Therefore, a circle fits the given description of a set of coplanar points with a constant distance from a fixed point.
8.
What is the equation of the circle whose center is (-6, -15) and 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 square root of 5. Therefore, the equation of the circle is (x+6)^2 + (y+15)^2 = 5. Option 2 is the correct answer.
9.
What is the equation of the circle given this graph?
Correct Answer
A. Option 1
10.
Which of the following is the center and the radius of this graph?
Correct Answer
A. Center (0,0) radius= 6
Explanation
The correct answer is center (0,0) and radius= 6. This means that the graph is a circle with its center at the origin (0,0) and a radius of 6 units.