Question

1)What is the 4x^2=y^2+8y+32
answer= either hyperbola or parabola

2)The graph of which equation is a circle?
answer= 5x^2+10x+5y=9

3)Solve the system of equations by graphing x^2+y^2=16 and y= -x+4
answer= (4,0),(0,-4)

4)Find the exact solutions of each system of equations x^2+y^2=25 and 9y=4x^2
answer= (3,0),(-3,4)

5)Find the exact solutions of each system of equations y=x^2+1 and y=2x
answer= (1,2)

#1 is a hyperbola.
The ?x^2 - ?y^2 .... is the clue.

#2 your answer of
5x^2+10x+5y=9 is a parabola

#3
solutions are (4.0) and (0,4)
use substitition
x^2 + (-x+4)^2 = 16
etc

#4
I got (3,4) and (-3,-4), they work in both equations, yours dont.
I multiplied the circle equation by 4 to get
4x^2 + 4y^2 = 100, then replaced 4x^2=9 into that, etc

#5
yes