I have 4 questions (CONICS SECTIONS! (HYPERBOLAS, PARABOLAS, ELLIPSES and CIRCLES!!!))

1. For 9y^2-4x^2-18y+24x-63=0 What is the domain and range?
2. For y^2=8x, the vertex is (0,0, and focus is (2,0) and the directrix is x=-2 right?
3. (y-1)^2=-4(x+1), the vertex is (-1,1), the focus (0,1) and the directrix is x=2 right?
4. (x+2)^2=12y... what is the vertex, focus, directrix?

Please help, thank you!

Question

I have 4 questions (CONICS SECTIONS! (HYPERBOLAS, PARABOLAS, ELLIPSES and CIRCLES!!!))

1. For 9y^2-4x^2-18y+24x-63=0 What is the domain and range?
2. For y^2=8x, the vertex is (0,0, and focus is (2,0) and the directrix is x=-2 right?
3. (y-1)^2=-4(x+1), the vertex is (-1,1), the focus (0,1) and the directrix is x=2 right?
4. (x+2)^2=12y... what is the vertex, focus, directrix?

Please help, thank you!

anonymous · Answer

Please help guys.. :( I attempted these and I just need someone to confirm it.

tkhunny · Answer

What did you get on #1 after you completed the square in both x and y?

anonymous · Answer

$$\frac{( y-1)^2 }{ 4 }-\frac{ (x-3)^2 }{ 9 }=1$$

tkhunny · Answer

Okay.  I didn't check that.  I'll just trust you.  With the center of the hyperbola in hand, we'll need the vertices in order to determine the Domain and Range.  What are the Vertices?

anonymous · Answer

Wait, the answer is (3, -3) and (3, 5)

mertsj · Answer

Number 3 opens to the left. Therefore the focus should be 1 unit to the left of the vertex.

anonymous · Answer

Is the vertex right?

mertsj · Answer

Yes.  The focus is (-2,1) and the directrix is x = 0

mertsj · Answer

4.  Vertex (-2,0) Focus (-2,3) directrix y = -3

anonymous · Answer

Thank you so much, you have no idea how much you saved me.