Question

Find the center and foci of the ellipse: 9x2 + 16y² + 126x + 96y + 441 = 0

Answer 1

Center : ( –7 , –3 )

Focus 1: (–7 + √7 , –3 )

Focus 2: ( –7 –√7 , –3 )

`((x + 7)^(2) )/(16) + ((y + 3) ^(2) )/(9) = 1 \\ \frac{(x - h)^(2) }{ {a}^(2) } + \frac{(y - k)^(2) }{ {b}^(2) } = 1`

a= 4 , b= 3 , k = – 3 , h = –7

The center: ( h , k ) —> ( –7 , –3 )

`c = \sqrt{ {a}^(2) - {b}^(2) } = \sqrt{ {4}^(2) - {3}^(2) } \\ = √(16 - 9) = √(7)`

C = √7

Focus 1: ( h + c , k ) —> ( –7 + √ 7 , –3 )

Focus 2: ( h – c , k ) —> ( –7 –√7 , –3 )

I hope I helped you^_^