Question

Include center, vertices, co-foci and the hyperbola in yo ((y+1⁾²/(9)-((x-2)^(2))/(16)=1

Answer 1

The given equation represents a hyperbola with center, vertices, and co-foci. The equation in standard form is ((y + 1)² / 9) - ((x - 2)² / 16) = 1.

Step-by-step explanation:

The given equation represents a hyperbola in standard form. The center of the hyperbola can be found by using the values in the equation: (h, k) = (2, -1). The vertices can be calculated by adding/subtracting the square root of the denominators to/from the x-coordinate of the center: (-8, -1) and (12, -1). The co-foci can be found by using the value of c, which is the square root of the sum of the squares of the denominators: c ≈ 6.7082. The co-foci are located at (2 - c, -1) and (2 + c, -1).

The equation of the hyperbola in standard form is ((y + 1)² / 9) - ((x - 2)² / 16) = 1.