Question

Help me please!!?!?? ?

Answer 1

1

`3x^2 + 5y^2 - 12x + 30y + 42 = 0`

`3x^2 - 12x + 5y^2 + 30y = - 42`

`3(x^2 - 4x) + 5(y^2 + 6y) = -42`

`3(x^2 -4x + 4) + 5(y^2 + 6y + 9) = -42 + 12 + 45`

`3(x-2)^2 + 5(y+3)^2 = 15`

`((x-2)^2)/(5) + ((y+3)^2)/(3) = 1`

Ellipse, same signs different coefficients on
`x^2` and
`y^2`

2

`9x^2 -36x - 4y^2 + 8y = 4`

`9(x^2 - 4x + 4) - 4(y^2 - 2y + 1) = 4 + 36 - 4`

`9(x- 2)^2 - 4(y - 1^2) = 36`

Hyperbola, opposite signs on
`x^2` and
`y^2`

3

`y = x^2 +2x + 3 = (x + 1)^2 + 2`

parabola

4

`x^2 - 4 x + y^2 + 4y = 4`

`(x - 2)^2 + (y+2)^2 = 4 + 4 + 4 = 12`

equal coefficents on
`x^2` and
`y^2`, circle

5

`-9x^2 - 18x + 4y^2 - 8y = 41`

`-9(x^2 -2x + 1) + 4(y^2 - 2y + 1) = 41 - 9 + 4`

`-9(x-1)^2 + 4(y-1)^2 = 36`

hyperbola, opposite signs

6

`-4x = y^2 - 2y - 11 = (y-1)^2 - 12`

That's a parabola, sideways open to the left

7

`2(x^2 + 6x) + 3(y^2 - 8y) = -60`

`2(x^2 + 6x + 9) + 3(y^2 - 8y + 16) = -60 + 18 + 48`

`2(x+3)^2 + 3(y - 4)^2 = 6`

`((x+3)^2)/(3) + ((y-4)^2)/(2) = 1`

Ellipse, different coefficients

8

`16x^2 - 32x - y^2 - 6y = 57`

`16(x^2 - 2x + 1) - (y^2 + 6y + 9) = 57 + 16 - 9 = 64`

opposite signs, hyperbola

You'll have to do the graphing yourself, sorry