Center : ( –7 , –3 )
Focus 1: (–7 + √7 , –3 )
Focus 2: ( –7 –√7 , –3 )
[tex] \frac{(x + 7)^{2} }{16} + \frac{(y + 3) ^{2} }{9} = 1 \\ \frac{(x - h)^{2} }{ {a}^{2} } + \frac{(y - k)^{2} }{ {b}^{2} } = 1[/tex]
a= 4 , b= 3 , k = – 3 , h = –7
The center: ( h , k ) —> ( –7 , –3 )
[tex]c = \sqrt{ {a}^{2} - {b}^{2} } = \sqrt{ {4}^{2} - {3}^{2} } \\ = \sqrt{16 - 9} = \sqrt{7} [/tex]
C = √7
Focus 1: ( h + c , k ) —> ( –7 + √ 7 , –3 )
Focus 2: ( h – c , k ) —> ( –7 –√7 , –3 )
I hope I helped you^_^
