# Test On The Equation Of Circle

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| By Angcc2009
A
Angcc2009
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Quizzes Created: 2 | Total Attempts: 2,957
Questions: 5 | Attempts: 2,708

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A circle is a shape consisting of all points in a plane that are at a given distance from a given point, centre. The equation of circle is an important mathematical topic in the chapter of circles, and is a must to prepare for every exam. Take this quiz and improve your know about the equations of circle.

• 1.

### Find the equation of the circle with centre (-1, 2) and radius = 2 units.

• A.

Option 1

• B.

Option 1 and Option 3

• C.

Option 3

• D.

Option 2 and Option 3

• E.

None of the above

B. Option 1 and Option 3
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 (-1, 2) and the radius is 2 units. Plugging these values into the equation, we get (x+1)^2 + (y-2)^2 = 2^2. Simplifying further, we have (x+1)^2 + (y-2)^2 = 4. Therefore, the correct options are Option 1 and Option 3, as they represent the correct equation of the circle.

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• 2.
• A.

Centre = (2, 6)

• B.

Centre = (2, -4)

• C.

Centre = (-2, 4)

• D.

Centre = (-2, -4)

• E.

Centre = (2, 4)

E. Centre = (2, 4)
• 3.
• A.

Radius = 4 units

• B.

Radius = 5 units

• C.

Radius = 6 units

• D.

Radius = 7 units

• E.

None of the above

C. Radius = 6 units
• 4.

### Given that A = ( -2, 0) and B = (4, 8) and the line segment AB is the diameter of the circle. Find the equation of the circle.

• A.

Option 1 and Option 4

• B.

Option 2 and Option 3

• C.

Option 1 and Option 3

• D.

Option 2 and Option 4

• E.

None of the above

C. Option 1 and Option 3
Explanation
The equation of a circle can be found using the formula (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. Since the line segment AB is the diameter of the circle, the midpoint of AB will be the center of the circle. The midpoint of AB can be found using the midpoint formula, which is ((x1 + x2)/2, (y1 + y2)/2). Plugging in the values of A and B, we get the midpoint as ((-2 + 4)/2, (0 + 8)/2) = (1, 4). Therefore, the center of the circle is (1, 4). To find the radius, we can use the distance formula between A and B, which is sqrt((x2 - x1)^2 + (y2 - y1)^2). Plugging in the values of A and B, we get the radius as sqrt((4 - (-2))^2 + (8 - 0)^2) = sqrt(36 + 64) = sqrt(100) = 10. Therefore, the equation of the circle is (x - 1)^2 + (y - 4)^2 = 10^2, which simplifies to (x - 1)^2 + (y - 4)^2 = 100. This corresponds to Option 1 and Option 3.

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• 5.
6 , -6

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• Current Version
• May 21, 2024
Quiz Edited by
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• Jun 09, 2009
Quiz Created by
Angcc2009

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