Find the centre and radius of each of the following circles:
(x - 1)2 + y2 = 4
(i) Given that we need to find the centre and radius of the given circle (x - 1)2 + y2 = 4.
We know that the standard equation of a circle with centre (a, b) and having radius ‘r’ is given by:
⇒ (x - a)2 + (y - b)2 = r2 - - - - - (1)
Let us convert given circle’s equation into the standard form.
⇒ (x - 1)2 + y2 = 4
⇒ (x - 1)2 + (y - 0)2 = 22 ..... - (2)
Comparing (2) with (1), we get
⇒ Centre = (1, 0) and radius = 2
∴The centre and radius of the circle is (1, 0) and 2.