Answer:
1. -6
2. +9
3. +1
4. -6
5. +9
6. +1
7. -3
8. +1
9. 4
10. Circle
Step-by-step explanation:
1. For part 1, you just subtract the 6 from both sides of [tex]x^2+y^2-6x+2y+6=0[/tex] to get [tex]x^2-6x+y^2+2y=-6[/tex]
2. For part 2, this is where you complete the square. So we find [tex]b/2a[/tex] and we sqaure it.[tex]x^2-6x[/tex] is what we are given and [tex]a=1, b=6[/tex] meaning that [tex]6/2(1) = 3[/tex] and when we sqaure it, we get [tex]3^2=9[/tex] and we add it since the square of any negative number is positive.
3. For part 3, you complete the sqaure again . So we find [tex]b/2a[/tex] and we sqaure it. [tex]y^2+2y[/tex] is what we are given and [tex]a=1, b=2[/tex] meaning that [tex]2/(2*1) = 1[/tex] and when we sqaure it, we get [tex]1^2 = 1[/tex]and we add it since the square of any negative number is positive.
4. Refer to part one, since we subtracted 6 in the first step, this is where it is afterwards.
5. In part 2, we added 9 to the left side, meaning that we must add 9 to the right side so we get +9.
6. In part 3, we added 1 to the left side, meaning that we must add 1 to the right side so we get +1.
7. Now you just reverse foil since this is a sqaured polynomial:
[tex]x^2-6x+9[/tex] → [tex](x-3)^2[/tex] and -3 is the value asked.
8. Again, reverse foil since square polynomial:
[tex]y^2+2y+1[/tex] → [tex](y+1)^2[/tex] and +1 is the value asked
9. Find the sum of parts 4,5, and 6, and you will get 4 as the result :
[tex]-6+9+1=4[/tex]
10. Since the final equation is in the form
[tex](x-h)^2+(y-k)^2=r^2[/tex] and its the general form of a circle, the conic shown is a circle.
That's it!
