SOLUTION: Classify the coincs. 1. x2 -8x + y = -2 2. x2 + y2 - 6x - 10y = 2 3. x2 + 10x - 8y = -73 4. 9x2 - 4y2 + 54x + 8y + 41 = 0 5. 9x2 + 4y2 - 72x

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Question 759363: Classify the coincs.
1. x2 -8x + y = -2
2. x2 + y2 - 6x - 10y = 2
3. x2 + 10x - 8y = -73
4. 9x2 - 4y2 + 54x + 8y + 41 = 0
5. 9x2 + 4y2 - 72x - 32y = -172
6. 4x2 + 25y2 + 16x + 50y - 59 = 0
7. x2 + 2x +y2 + 6y = 15
Answer by DSMLMD(16) (Show Source):
You can put this solution on YOUR website!
1.
x^2-8x+y = -2
(x^2-8x+16) = -2 - y
(x-4)^2 - 16 = -2 - y
(x-4)^2 = 14 - y
(x-4)^2 = -(y - 14)
it's parabola

2.
x^2+y^2-6x-10y=2
x^2-6x+y^2-10y=2
(x^2-6x+9)+(y^2-10y+25)=2
(x-3)^2 - 9 + (y-5)^2 - 25 = 2
(x-3)^2 + (y-5)^2 = 32
it's circle

3.
x^2+10x-8y=-73
(x^2+10x+25)=8y-73
(x+5)^2 - 25 = 8y-73
(x+5)^2 = 8y-48
(x+5)^2 = 8(y-8)
it's parabola

4.
9x^2 - 4y^2 + 54x + 8y + 41 = 0
9x^2 + 54x - 4y^2 + 8y + 41 = 0
9(x^2 + 6x) - 4(y^2 - 2y) = -41
9(x^2 + 6x + 9) - 4(y^2 - 2y + 1) = -41
9(x + 3)^2 - 81 - 4(y - 1)^2 + 4 = -41
9(x + 3)^2 - 4(y - 1)^2 = 36
(x + 3)^2/4 - (y - 1)^2/9 = 1
it's hyperbola

5.
9x^2 + 4y^2 - 72x - 32y = -172
9x^2 - 72x + 4y^2 - 32y = -172
9(x^2 - 8x) + 4(y^2 - 8y) = -172
9(x^2 - 8x + 16) + 4(y^2 - 8y + 16) = -172
9(x - 8)^2 - 144 + 4(y - 8)^2 - 144 = -172
9(x - 8)^2 + 4(y - 8)^2 = 36
(x - 8)^2/4 + (y - 8)^2/9 = 1
it's ellipse

6.
4x^2 + 25y^2 + 16x + 50y - 59 = 0
4x^2 + 16x + 25y^2 + 50y - 59 = 0
4(x^2 + 4x) + 25(y^2 + 2y) = 59
4(x^2 + 4x + 4) + 25(y^2 + 2y + 1) = 59
4(x + 4)^2 - 16 + 25(y + 1)^2 - 25 = 59
4(x + 4)^2 + 25(y + 1)^2 = 100
(x + 2)^2/25 + (y + 1)^2/4 = 1
it's ellipse

7.
x^2 + 2x + y^2 + 6y = 15
(x^2 + 2x + 1) + (y^2 + 6y + 9) = 15
(x + 1)^2 + 1 + (y + 3)^2 + 3 = 15
(x + 1)^2 + (y + 3)^2 = 11
it's circle

SOLUTION: Classify the coincs. 1. x2 -8x + y = -2 2. x2 + y2 - 6x - 10y = 2 3. x2 + 10x - 8y = -73 4. 9x2 - 4y2 + 54x + 8y + 41 = 0 5. 9x2 + 4y2 - 72x - 32y = -172 6. 4x2