Question

What are the foci of (x+10)^2/25-(y+1)^2/9=1?


(-1 ±√(34) , -10)

(-1, -10 ±√(34))

(-10 ±√(34) , -1)

(-10, -1 ±√(34))

Answer 1

This time it's a horizontal hyperbola, with center (h, k) which is (-10, -1). Foci of a horizontal hyperbola:

\[(h \pm c, k)\]

c is the distance from the center to the focus, and is given by

c^2 = a^2 + b^2

Answer 2

a^2 = 25, b^2 = 9

Answer 3

Standard form for horizontal hyperbola is:
\[\frac{ (x-h)^2 }{ a^2 } - \frac{ (y-k)^2 }{ b^2 } = 1\]