how to do this ellipse problem???

Question

how do you find the center, foci, major & minor axis?

maybe u can give me an example such as on these problems-
#1 9x^2 + 10y^2 + 54x + 20y= -1

#2 2x^2 + y^2 - 4x + 8y - 6=-

Answer 1

All your questions answered:

http://mathworld.wolfram.com/Ellipse.html

Mathworld has been a great aid to me throughout my college life.

Answer 2

Given the equation for an ellipse

(x + h)²/a² + (y + k)²/b² = 1

The center is (h,k).

a = semi-major axis
b = semi-minor axis

2a = major axis
2b = minor axis

c² = a² - b²
c = √(a² - b²)

The foci run along the major axis (which in this case is horizontal) and are (h-c,k) and (h+c,k).

Now apply the principles to the problem at hand.
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#1)
9x² + 10y² + 54x + 20y = -1

First put the equation into standard form for an ellipse.

9(x² + 6x + 9) + 10(y² + 2y + 1) = -1 + 9*9 + 10*1
9(x + 3)² + 10(y + 1)² = -1 + 81 + 10 = 90
(x + 3)²/10 + (y + 1)²/9 = 1

The center of the ellipse is (-3,-1).

a = √10
b = √9 = 3

Major axis = 2a = 2√10
Minor axis = 2b = 6

c² = a² - b² = 10 - 9 = 1
c = 1

The foci run along the major axis (which in this case is horizontal) and are (-3-1,-1) and (-3+1,-1) or
(-4,-1) and (-2,-1).

Use the same principles for #2.