Question

Identify the location of the foci.

Answer 1

Hi,

Explanation:

Because your problem is too long,

i will only do the first one: n°10

1. reduce the equation, finding the center

`18y^2-7x^2+72y+42x-117=0\\\\18(y^2+4y+4)-7(x^2-6x+9)-117-72+63=0\\\\18(y+2)^2-7(x-3)^2=126\\\\\boxed{\frac{{(x-3)}^2}{18} -\frac{{(y+2)}^2}{7}=-1\\}\\`

2. The hyperbola is vertical

Center is (3,-2)

Focus 's distance= √(18+7)=5

Foci are (3,3=-2+5), and (3,-7)

For n°12: reduced equation is

`\frac{{(x-2)}^2}{25} -\frac{{(y+4)}^2}{16} =-1\\`