Question

Find the foci of the hyperbola defined by the equation $\frac{(x+8)^{2} }{9} - \frac{(y-7)^{2} }{25} =1$ . If necessary, round to the nearest tenth.

Answer 1

Answer:

Foci:   (-2.2, 7) and (-13.8, 7)

(nearest tenth)

Step-by-step explanation:

General equation of a hyperbola

$\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1$

Center:  (h, k)

Focal length equation:  a² + b² = c²

Foci:  (h ± c, k)

Given equation:

$\dfrac{(x+8)^2}{9}-\dfrac{(y-7)^2}{25}=1$

⇒ h = -8

⇒ k = 7

⇒ a² = 9

⇒ b² = 25

Focal length:

⇒ a² + b² = c²

⇒ 9 + 25 = c²

⇒ c = √34

Foci:  

⇒ (h ± c, k) = (-8 ± √34, 7)

                  = (-2.2, 7) and (-13.8, 7)

**Refer to the attached graph**

Asymptotes are in red

Foci are in blue