Question

What is the equation of the parabola with the vertex (4,4) and focus (7,4)?

Answer 1

The bot is wrong.

the equation should be :
(x - 4) = 12(y - 4)^2

My equation has a vertex of (4,4) and a focus at (7,4)

the bot's equation would have a vertex of (4,4) and a focus at (4,7)

Answer 2

Since the vertex is to the left of the focus, we know that the parabola opens to the left. The standard form equation for a parabola with vertex (h,k) and focus (h+c,k) is:

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

where c is the distance from the vertex to the focus. In this case, h=4, k=4, and c=3. Substituting these values, we get:

(x - 4)^2 = 4(3)(y - 4)

Simplifying further, we get:

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

This is the equation of the parabola.

Answer 3

You are correct, I apologize for the error. The equation for a parabola with vertex (4,4) and focus (7,4) is:

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

Alternatively, if we solve for x instead, the equation becomes:

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

Thank you for bringing this to my attention.