Find the centre and the radius of the circle which is concentric to the circle $x^{2} + y^{2} - 16 = 0$ having radius double of the radius of the given circle.

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Solution

Comparing the given equation $x^{2} + y^{2} - 16 = 0 \Rightarrow x^{2} + y^{2} = 16 \Rightarrow x^{2} + y^{2} = 4^{2}$
with the general equation for the circle centered at origin i.e., $x^{2} + y^{2} = r^{2}$ ,
we get, radius of the given circle, r = 4 units.

We are required to find centre and radius of a circle concentric to the given circle and with radius its double.
So, radius of the required circle will be $2 \times 4 = 8 u n i t s .$
And we know that concentric circles will have same centre which will be origin in this case. So, centre of the required circle = (0, 0).

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