Posted by Jeremy on Monday, August 17, 2009 at 2:15pm.
1.
9y^2+4x^2 - 108y+24x= -144
9(y-6)²-9*6² + 4(x+3)²-4*3² = -144
9(y-6)² + 4(x+3)²= -144 + 324 + 36
9(y-6)² + 4(x+3)²= (6√6)²
((y-6)/(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(x-h)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^2-108y+24x=-144, determine the center
i think it is a hyperbola
nvm that last post, i thought this was hw help
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