Q4 of 38 Page 730

Show that the equation x2 + y2 + 2x + 10y + 26 = 0 represents a point circle. Also, find its centre.

The general equation of a circle:


x2 + y2 + 2gx + 2fy + c = 0…(i) where c, g, f are constants.


Given, x2 + y2 + 2x + 10y + 26 = 0


Comparing with (i) we see that the equation represents a circle with 2g = 2g = 1, 2f = 10f = 5 and c = 26.


Centre ( - g, - f) = ( - 1, - 5).


Radius =




Thus it is a point circle with radius 0.


More from this chapter

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2

Show that the equation x2 + y2 + x – y = 0 represents a circle. Find its centre and radius.

 3

Show that the equation 3x2 + 3y2 + 6x - 4y – 1 = 0 represents a circle. Find its centre and radius.

 5

Show that the equation x2 + y2 - 3x + 3y + 10 = 0 does not represent a circle.

 6

Find the equation of the circle passing through the points

(i) (0, 0), (5, 0) and (3, 3)


(ii) (1, 2), (3, - 4) and (5, - 6)


(iii) (20, 3), (19, 8) and (2, - 9)


Also, find the centre and radius in each case.