1.

If the equation of the circle is ax2 + (2a - 3)y2 - 4x + 6y - 1=0, then find the coordinates of the centre.

Answer»

ax2 + 2hxy +  by2 + 2g x + 2fy + c = 0 is represent a circle 2h = 0 and a = b.  

If ax2 + (2a - 3)y2 - 4x + 6y - 1=0 is the equation of the circle  

Here  a = 2a - 3  a = 3  

Then 3x2 + 3y2 - 4x + 6y - 1 = 0  

x2 + y2 - 4 x/ 3 + 6y / 3 - 1 / 3 = 0  

Center = ( -g / a , -f / a)  

Center = ( 2 / 3 ,-1)



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