Q2 of 101 Page 24

Find the centre and radius of each of the following circles:

x2 + y2 - x + 2y - 3 = 0

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.


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