Equation Of A Circle

25 July 2022
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10 test answers

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question
Which equation represents a circle with the same center as the circle shown but with a radius of 2 units?
answer
(x - 4)2 + (y - 5)2 = 4
Explanation: The equation for a circle with a radius of 2 units and the same center as the circle shown would be:x^2 + y^2 = 4
question
In the diagram, a circle centered at the origin, a right triangle, and the Pythagorean theorem are used to derive the equation of a circle, x2 + y2 = r2. If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle, which could represent the equation of the new circle?
answer
(x - h)2 + (y - k)2 = r2
Explanation: In the new scenario, the center of the circle is moved to the point (h, k), and the point P at (x, y) remains on the edge of the circle. The equation of the new circle can be represented as (x-h)2 + (y-k)2 = r2.
question
Which equation represents a circle with a center at (-3, -5) and a radius of 6 units?
answer
(x + 3)Β² + (y + 5)Β² = 36
Explanation: The equation for a circle with a center at (-3, -5) and a radius of 6 units is (x + 3)^2 + (y + 5)^2 = 36.
question
Which equation represents a circle that contains the point (-2, 8) and has a center at (4, 0)?
answer
(x - 4)2 + y2 = 100
Explanation: The equation of a circle with center at (4, 0) and radius 6 is (x - 4)^2 + (y - 0)^2 = 36.
question
Which point is on the circle centered at the origin with a radius of 5 units?
answer
(2, √ Μ…21)
question
What is the radius of a circle whose equation is x2 + y2 + 8x - 6y + 21 = 0?
answer
2
Explanation: There is no definitive answer to this question because it depends on how the circle is oriented in relation to the coordinate plane. If the circle is centered on the origin, then its radius would be 3. However, if the circle is not centered on the origin, then its radius could be any value that satisfies the equation.
question
The center of a circle represented by the equation (x + 9)2 + (y βˆ’ 6)2 = 102 is
answer
(-9,6)
Explanation: at (9, 6)The center of a circle is the point where the circle's radius meets the circle. In the equation (x+9)2 + (y-6)2 = 102, the center is at (9,6) because that is where the radius meets the circle. The radius is the distance from the center to any point on the circle, so in this equation, the radius is 10.
question
Which equation represents a circle with a center at (-4, 9) and a diameter of 10 units?
answer
(x + 4)2 + (y - 9)2 = 25
Explanation: The equation x^2 + y^2 = 100 represents a circle with a center at (0, 0) and a diameter of 10 units. To find an equation for a circle with a center at (-4, 9) and a diameter of 10 units, we can use the fact that the center of the circle is 4 units to the left of the center of the new circle and 9 units above the center of the new circle. This means that the equation for the new circle is (x + 4)^2 + (y - 9)^2 = 100.
question
What is the center of a circle whose equation is x2 + y2 + 4x - 8y + 11 = 0?
answer
(-2,4)
Explanation: The center of a circle is the point where the circle's radius meets the circle. In the case of a circle with equation x2 + y2 + 4x - 8y + 11 = 0, the center is the point (2, -4).
question
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Check all that apply.
answer
x^{2}+(y-3)^{2}=36 x^{2}+(y+8)^{2}=36
Explanation: There are several equations that could represent a circle with a diameter of 12 units and a center that lies on the y-axis. Some examples include:(x-6)^2 + (y-0)^2 = 144(x-0)^2 + (y-6)^2 = 144(x-12)^2 + (y-0)^2 = 144(x-0)^2 + (y-12)^2 = 144These are just a few examples, but there are many other possibilities.