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Question 48380: Please im asking for some help in solving the following. I would really and truly appreciate some help from you guys.Cheers.
1)What is the graph of the equation 6x2 - 24x - 5y2 - 10y - 11 = 0?
a. parabola
b. circle
c. ellipse
d. hyperbola
2)What is the graph of the equation 5x2 + 2y2 + 30x - 16y + 67 = 0?
a. parabola
b. circle
c. ellipse
d. hyperbola
3)What is the graph of the equation x2 + y2 - 8x + 6y + 24 = 0?
a. parabola
b. circle
c. ellipse
d. hyperbola
4)What is the graph of the equation x2 + 2x + 7 - y = 0?
a. parabola
b. circle
c. ellipse
d. hyperbola
5)Identify the solutions to the system of equations:
x2 + y2 = 25
16x2 + 25y2 = 400
a. no solutions
b. (5, 0)
c. (-5, 0)
d. (5, 0) and (-5, 0)
7)Identify the solutions to the system of equations:
y2 - x2 = 16
x2 - y2 = 16
a. no solutions
b. (4, 0)
c. (-4, 0)
d. (4, 0) and (-4, 0)
Answer by Nate(3500)   (Show Source):
You can put this solution on YOUR website! 1)What is the graph of the equation 6x2 - 24x - 5y2 - 10y - 11 = 0?
a. parabola
b. circle
c. ellipse
d. hyperbola
You are subtracting the squared variables, so the answer is (d.).
2)What is the graph of the equation 5x2 + 2y2 + 30x - 16y + 67 = 0?
a. parabola
b. circle
c. ellipse
d. hyperbola
You are adding the squared variables and the coefficients are different, so the answer is (c.).
3)What is the graph of the equation x2 + y2 - 8x + 6y + 24 = 0?
a. parabola
b. circle
c. ellipse
d. hyperbola
The coefficients are the same and both the squared variables are being added, so the answer is (b.).
4)What is the graph of the equation x2 + 2x + 7 - y = 0?
a. parabola
b. circle
c. ellipse
d. hyperbola
Since there is only one variable that is squared, this is (a.) the parabola.
5)Identify the solutions to the system of equations:
a. no solutions
b. (5, 0)
c. (-5, 0)
d. (5, 0) and (-5, 0)
x2 + y2 = 25 which can mean: y2 = 25 - x2
16x2 + 25y2 = 400
plug: 16x2 + 25(25 - x2) = 400
16x2 + 625 - 25x2 = 400
-9x2 = -225
x2 = 25
x = +- 5
plug: x2 + y2 = 25
y2 = 0
y = 0
P(5,0) and P(-5,0)
The answer is (d.).
7)Identify the solutions to the system of equations:
a. no solutions
b. (4, 0)
c. (-4, 0)
d. (4, 0) and (-4, 0)
y2 - x2 = 16 which means: y2 = x2 + 16
x2 - y2 = 16
plug:
x2 - x2 - 16 = 16
-16 = 16 No Solutions
The answe is (a.).
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