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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 $$x^2+y^2+4x-21=0$$
We have,
$$radius =5$$
And the centre lies on $$x-axis$$.

Let the centre $$(h, 0)$$

Therefore,
$$(x-h)^2+y^2=5^2$$

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

Then,
$$(2-h)^2+3^2=25$$
$$(2-h)^2=16$$
$$2-h=4$$
$$h=-2$$

So, the centre will be $$(-2, 0)$$

Therefore, the equation of the circle
$$(x+2)^2+y^2=25$$
$$x^2+4+4x+y^2=25$$
$$x^2+y^2+4x-21=0$$

Hence, this is the answer.

Maths

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