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Question

Find the equation of the circle with radius 5 whose centre lies on x-axis and passes through the point (2,3).

A
x2+y2+4x20=0
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B
x2+y2+4x21=0
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C
x2+y2+2x21=0
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D
x2y2+4x21=0
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Solution

The correct option is C x2+y2+4x21=0
We have,
radius=5
And the centre lies on xaxis.

Let the centre (h,0)

Therefore,
(xh)2+y2=52

Since, the circle passes through the point (2,3)

Then,
(2h)2+32=25
(2h)2=16
2h=4
h=2

So, the centre will be (2,0)

Therefore, the equation of the circle
(x+2)2+y2=25
x2+4+4x+y2=25
x2+y2+4x21=0

Hence, this is the answer.

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