SOLUTION: Please im asking for your guys devine help.Your assisstance would be very very important to me.So please offer me a helping hand. 1)Find the foci of an ellipse with the equation

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Question 48322: Please im asking for your guys devine help.Your assisstance would be very very important to me.So please offer me a helping hand.
1)Find the foci of an ellipse with the equation 7(x - 2)2 + 3(y - 2)2 = 21.
2)Find the slopes of the asymptotes of a hyperbola with the equation y2 = 36 + 4x2.
3)What is the graph of the equation 6x2 - 24x - 5y2 - 10y - 11 = 0?
4)What is the graph of the equation 5x2 + 2y2 + 30x - 16y + 67 = 0?
5)What is the graph of the equation x2 + y2 - 8x + 6y + 24 = 0?
6)What is the graph of the equation x2 + 2x + 7 - y = 0?
7)Identify the solutions to the system of equations:
y2 - x2 = 16
x2 - y2 = 16
8)Identify the solutions to the system of equations:
x2 + y2 = 25
16x2 + 25y2 = 400
Answer by Nate(3500) (Show Source):
You can put this solution on YOUR website!
1)Find the foci of an ellipse with the equation
7(x - 2)2 + 3(y - 2)2 = 21
(x - 2)^2/3 + (y - 2)^2/7 = 1
a = 7
b = 3

Vertical ellipse, so the increasement is due to 'y'
Center: (2,2)
Foci: (2,2+) and (2,2-)
2)Find the slopes of the asymptotes of a hyperbola with the equation
y^2 = 36 + 4x^2
y^2 - 4x^2 = 36
y^2/36 - x^2/9 = 1
Vertical hyperbola, so the slope of the asymptotes = +- a/b
a = 36 and b = 9
Slope = +- 36/9 = +- 4
3)What is the graph of the equation
6x^2 - 24x - 5y^2 - 10y - 11 = 0
(6x^2 - 24x) + (-5y^2 - 10y) = 11
6(x^2 - 4x) - 5(y^2 + 2y) = 11
6(x - 2)^2 - 5(y + 1)^2 = 11 + 24 + 5 = 40
(x - 2)^2/(20/3) - (y + 1)^2/8 = 1

4)What is the graph of the equation
5x^2 + 2y^2 + 30x - 16y + 67 = 0
5x^2 + 30x + 2y^2 - 16y = -67
(5x^2 + 30x) + (2y^2 - 16y) = -67
5(x^2 + 6x) + 2(y^2 - 8y) = -67
5(x + 3)^2 + 2(y - 4)^2 = -67 + 45 + 32 = 10
(x + 3)^2/2 + (y - 4)^2/5 = 1

5)What is the graph of the equation
x^2 + y^2 - 8x + 6y + 24 = 0
x^2 - 8x + y^2 + 6y = -24
(x - 4)^2 + (y + 3)^2 = -24 + 16 + 9 = 1

6)What is the graph of the equation
x^2 + 2x + 7 - y = 0
(x + 1)^2 = y - 6
(x + 1)^2 + 6 = y

7)Identify the solutions to the system of equations:
y^2 - x^2 = 16 can mean: y^2 = x^2 + 16
x^2 - y^2 = 16 cane mean when plugged: x^2 - x^2 - 16 = 16 which is -16 = 16
No Solutions
8)Identify the solutions to the system of equations:
x^2 + y^2 = 25 which can mean: x^2 = 25 - y^2
16x^2 + 25y^2 = 400 plug~~~>
16(25 - y^2) + 25y^2 = 400
400 - 16y^2 + 25y^2 = 400
9y^2 = 0
y^2 = 0
y = +- 0
plug~~~>
x^2 + y^2 = 25
x^2 = 25
x = +- 5
Solutions: (0,5) and (0,-5)