In the following exercises, identify the type of graph.

1. $x=-y^2-2y+3$
   
2. $9y^2-x^2+18y-4x-4=0$
   
3. $9x^2+25y^2=225$
   
4. $x^2+y^2-4x+10y-7=0$
   

The equations are

1. $x=-y^2-2y+3$
   
2. role="math" localid="1646029866766" $9y^2-x^2+18y-4x-4=0$
   
3. role="math" localid="1646030038276" $9x^2+25y^2=225$
4. role="math" localid="1646030166290" $x^2+y^2-4x+10y-7=0$

Identify the graph of the equation.

The equation is $x=-y^2-2y+3$

Here, only one variable y is squared. so equation represent parabola.

The equation is $9y^2-x^2+18y-4x-4=0$

x² and y² terms have different signs, different coefficients, so the equation represents hyperbola.

The equation is $9x^2+25y^2=225$

x and y both terms are squared and have the same coefficients, So, the equation represents circle.

The equation is $x^2+y^2-4x+10y-7=0$

x and y both the terms are squared and have the same sign, different coefficients, So the equation represents ellipse.