Given that we need to find the centre and radius of the given circle x² + y² - x + 2y - 3 = 0.

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.

⇒ x² + y² - x + 2y - 3 = 0

⇒

⇒

⇒ - - - - - (2)

Comparing (2) with (1), we get

⇒ Centre = (, - 1) and radius =

∴The centre and radius of the circle is (, - 1) and.