Pre Cal.
posted by Jeremy on .
1. Identify the conic section represented by: 9y^2+4x^2  108y+24x= 144?
Is it ellipse.
2. Find the coordinates of the vertex and the equation of the axis of symmetry for the parabola represented by: x^2 + 4x  6y + 10 = 0.
vertex: (2 , 1)
axis of symmetry: x = 2

1.
9y^2+4x^2  108y+24x= 144
9(y6)²9*6² + 4(x+3)²4*3² = 144
9(y6)² + 4(x+3)²= 144 + 324 + 36
9(y6)² + 4(x+3)²= (6√6)²
((y6)/(2√6))² + ((x+3)/(3√6))²= 1
Does that ring a bell?
2.
This is done by completing the square:
x^2 + 4x  6y + 10 = 0.
y=(x^2 + 4x + 10)/6
=(1/6)(x+2)²+1
=a(xh)²+k (a=1/6, h=2, k=1)
(h,k) is the vertex.
The equation of the axis of symmetry is
x=h 
identify the conic
9 y^2+4y^2108y+24x=144, determine the center
i think it is a hyperbola 
nvm that last post, i thought this was hw help