The equation of a parabola is given by (x - 4)^2 = 12(y + 1). What is the y-coordinate of … — ACT

The equation of a parabola is given by $(x - 4)^2 = 12(y + 1)$ . What is the $y$ -coordinate of the focus of this parabola?

Answer: 2

The correct answer is 2.

The equation

(x - 4)^2 = 12(y + 1)

is a parabola with a vertical axis of symmetry, vertex at

(4, -1)

, and focal length

p = 3

. The focus is located

p

units above the vertex, yielding a

y

-coordinate of

-1 + 3 = 2

Identify the standard form of the parabola's equation.

The equation

(x - 4)^2 = 12(y + 1)

matches

(x - h)^2 = 4p(y - k)

This form allows us to find the vertex and the focal distance

p

directly.

Determine the vertex and focal distance

p

The vertex is

(4, -1)

and

p = 3

since

4p = 12

Matching the given equation terms to the standard form reveals these properties.

Find the coordinates of the focus.

The focus is at

(4, 2)

The focus is located

p

units vertically above the vertex for a parabola opening upward.

Focus of a Parabola

Question