Question

What are the coordinates of the foci of the conic section shown below? 2 (x + 2)2 (1-3) 16 (x + ) _ ) = 1 9 B. O A. (-2,3+5) O B.(-2+17,3 ) OC O c. (-2+5,3) o D. (2,3+77) 2

Answer 1

The given conic section is a hyperbola since this type of conic section can be represented by the equation:

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

And the foci of a hyperbola with center at (h, k) are given by:

(h + c, k) and (h - c, k),

where

c = √(a² + b²)

So, for this hyperbola, we have:

h = -2

k = 3

a² = 16

b² = 9

Then, c is given by:

c = √(16+9) = √25 = 5

And the foci are:

(h + c, k) = (-2 + 5, 3) = (3, 3)

and

(h - c, k) = (-2 - 5, 3) = (-7, 3)

Thus, we can write the coordinates of both the foci as:

(-2 ± 5, 3)

Therefore, option C is correct.