$$-4\left(x+\frac{1}{2}\right)^2=y$$  

$$81x^2-8,100=-100y^2$$  

$$2-x^2-y^2=0$$  

$$144=16x^2-9y^2$$  

$$9y^2-72x+6y+361=0$$  

$$4x^2=-y^2-4$$  

$$\left(x-3\right)^2=\frac{\left(y-1\right)^2}{25}-1$$  

$$9y^2-x^2+18y+6x=0$$  

$$x^2=4\left(y+2x\right)$$  

$$9y^2+36=x^2+36y+6$$  

$$\frac{1}{2}x^2+\frac{1}{8}y^2=\frac{1}{4}$$  

$$-x=\frac{y^2}{32}$$  

$$\frac{y^2}{3}-1=\frac{x^2}{6}$$  

$$x^2+\left(y+2\right)^2-5=0$$