Circles, when Coordinates of the Centre and Radius Are Given

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When Coordinates of the Centre and Radius Are Given

What happens when the

  • Circle passes through the origin?

  • Circle does not pass through origin and the centre lies on the x-axis?

  • Circle passes through origin and the x-axis is a diameter?

  • Centre of the circle is origin?

  • Circle touches the x-axis?

  • Circle touches the y-axis?

  • Circle touches both the axes?

We shall try to find the answer of the above questions one by one.

In this case, since satisfies , we get

Hence the equation reduces to

In this case

Hence the equation reduces to

In this case and (see Fig.)

In case of Circle k=0

In Case of Circle K=0

In case of Circle k=0

Hence the equation reduces to

(iv) In this case , Hence the equation reduces to

(v) In this case see Fig.)

In case of Circle k=a

In Case of Circle K=A

In case of Circle k=a

Hence the equation reduces to

(vi) In this case

Hence the equation) reduces to

(vii) In this case . (See Fig.)

In case of Circle h=k=a

In Case of Circle H=K=A

In case of Circle h=k=a

Hence the equation) reduces to

Example:

Find the equation of the circle whose centre is ) and radius is .

Solution:

Comparing the terms given in equation), we have

and .

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