Question

\dfrac{x^2}{46}+\dfrac{(y+8)^2}{26}=1 46 x 2 ​ + 26 (y+8) 2 ​ =1start fraction, x, squared, divided by, 46, end fraction, plus, start fraction, left parenthesis, y, plus, 8, right parenthesis, squared, divided by, 26, end fraction, equals, 1 What are the foci of this ellipse? Choose 1 answer:

Answer 1

The focus of the ellipse are;

(-12·√(10), -8) and (12·√(10), -8)

Explanation:

The given equation for the ellipse is presented as follows;

`(x^2)/(46) + ((y + 8)^2)/(26) = 1`

From the general equation of the ellipse, we have;

`((x - h)^2)/(a^2) + ((y - k)^2)/(b^2) = 1`

The focus of the ellipse are, (h - c₁, k) and (h + c₁, k)

By comparison, we get;

h = 0, k = -8, a = 46, b = 26

We have;

c² = a² - b²

c² = 46² - 26² = 1440

c = 12·√(10)

The focus of the ellipse are therefore;

(0 - 12·√(10), -8) = (-12·√(10), -8), and (0 + 12·√(10), -8) = (12·√(10), -8).