Question

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.

• A. Centre = (2, 2)
  Radius = 4 units
• B. Centre = (0, 0)
  Radius = 8 units
• C. Centre = (0, 0)
  Radius = 16 units
• D. Centre = (2, 2)
  Radius = 8 units

Answer 1

The correct option is B Centre = (0, 0)

Radius = 8 units
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 $2\times 4=8units.$
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).