If I could have a step by step process on these problems that would be fantastic.?

Question

1. Find the center (h,k) of the circle with the equation x^2+y^2-6y=7

2. How would you graph (y-1)^2=6(x+2) If I could have you show me step by step process and a very clear explanation on this particular problem, that would be great.

3. How do I find the standard form for the equation of the hyperbola whose center is (0,0), which has vertices's at the points (-6,0) and (6,0), and which passes through the point (10,4).

4. Here is another, find the equation of the hyperbola whose vertices's are at (3,-1) and (9,-1), and which has a focus at (1,-1).

Thanks to all who answer sincerely

Answer 1

For a nice step-by-step, see the following site...scroll down to circle, ellipse and hyperbola section

http://www.analyzemath.com/PrecalculusTutorials.html

I recommend you write a note-sheet with each of the standard forms of the equations, both with center at (0,0) and at (h,k). Then define your terms like vertices and focus in terms of a,b,c or h,k depending.

Answer 2

1) Start with x^2+y^2-6y=7
Then complete the squares (add 9 to both sides) to get:
x^2 + (y-3)^2 = 16
So the center is (0,3) (the radius is 4).

2) It is a parabola, with vertex at (-2,1)

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