Tel which conic is defined by each equation
4x^2+4y^2-9y+1=0... I know it defines a circle but I need help completing the square because I have to find out if real solutions exist, my book skips through completing the square :/ please help

Question

Tel which conic is defined by each equation
4x^2+4y^2-9y+1=0... I know it defines a circle but I need help completing the square because I have to find out if real solutions exist, my book skips through completing the square :/ please help

anonymous · Answer

$$4x^2 + 4y^2 - 9y + 1 = 0$$$$x^2 + y^2 - \frac{9}{4}y + \frac{1}{4} = 0$$$$x^2 + y^2 - \frac{9}{4}y = -\frac{1}{4}$$$$x^2 + y^2 - \frac{9}{4}y + \frac{81}{64} = -\frac{1}{4} + \frac{81}{64}$$$$x^2 + \left( y - \frac{9}{8} \right)^2 = \frac{65}{64}$$

anonymous · Answer

I love you... lol no but really thanks a lot!