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GeoGebra

CircleIntro

Author:Ajay Kumar Otta

EQUATION OF A CIRCLE

Circle is the locus of a point which moves such that its distance from a fixed point is constant. The fixed point is called the centre of the circle and the distance of any point on the circle from the centre is called the radius of the circle. Let be the centre of the circle and let be any point on the circle with radius . Then we have or . In the applet below drag the centre C or change the coordinates of Centre in the input box . Similarly change the radius in the input box or by the slider. Observe the changes in its equation. For answering the questions use the applet.
To answer the following questions you may drag the centre C in the above applet to appropriate positions and use the radius slider or you may use the input boxes straight away.

Q.1

Find the equation of the circle in the first quadrant which touches both the x and y axes with radius 2.

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Q.2

Find the equation of the circle in the second quadrant which touches both the axes and has radius 3.

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Q.3

Find the equation of the circle in the third quadrant which touches both the axes and has radius 2.

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Q.4

Find the equation of the circle in the fourth quadrant which touches both the axes and has radius 1.

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Q.5

Find the equation of the circle in the first quadrant which touches the x axis only and has centre (4,2).

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Q.6

Find the equation of the circle in the first and fourth quadrant whose centre lies on x-axis and has radius 3.

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Q.7

The circle

Select all that apply
  • A
  • B
  • C
  • D
  • E
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Q.8

Origin lies in the interior of the circle with centre (4,4) and radius 5. True/False

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  • A
  • B
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Q.9

The circle with centre (8,2) and radius 2 touches the x-axis at (8,0). True/False

Select all that apply
  • A
  • B
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Q.10

The circle with centre (2,-4) and radius 2 touches the y-axis at (-4,0). True/False

Select all that apply
  • A
  • B
Check my answer (3)

Let us have more practice.

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