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What is the equation to circle which touches both the axes and radius is 5?

What is the equation to circle which touches both the axes and radius is 5? Correct Answer x<sup>2</sup> + y<sup>2</sup> - 10x - 10y + 25 = 0

Concept:

Equation of circle having centre (h, k) and radius r is (x – h)2 + (y – k)2 = r2

Calculation:

Here, circle touching both the axes. Let it touches at (a, 0) and (0, a), so centre will be (a, a)

Now, Radius = a = 5

So, centre = (5, 5) and radius = 5

Now, Equation of circle having centre (5, 5) and radius 5

(x - 5)2 + (y - 5)2 = 52

⇒ x2 + 25 - 10x + y2 + 25 - 10y = 25

⇒ x2 + y2 - 10x - 10y + 25 = 0

Hence, option (2) is correct. 

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