Question

what are the coordinates of the vertices of the conic section shown below? (x+2)^2/16-(y-3)^2/9=1

A.) (-6,3) and (2,3) B.) (-2,-1) and (-2,7) C.) (-2,3) and (6,3) D.) (-2,-7) and (-2,1)

Answer 1

The standard form of the equation of a hyperbola with center (h, k) (where a and b are not equals to 0) is (x - h)²/a² - (y - k)²/b² = 1 (Transverse axis is horizontal) or (y - k)²/a² - (x - h)²/b² = 1 (Transverse axis is vertical).

The relation between a, b and c is b² = c² - a².

Compare the equation (x + 2)²/4² - (y - 3)²/3² = 1 with (x - h)²/a² - (y - k)²/b² = 1.

a = 4, b = 3, h = - 2 and k = 3.

Center = (h, k) = (- 2, 3),
 

Vertices = (h ± a, k) = (- 2 ±4, 3) = (2, 3) and (- 6, 3),

Option (1) is correct