Question

Answer Problem using the figure.

If a = 4, then the coordinates of the focus are___________.

Short answer

If a = 4, then the coordinates of the focus are (3, 6).

Step-by-step solution

Step 1. Given information.

We have given graph is,

Step 2. Concept used.

Focus of the parabola:

A parabola represents the locus of a point that is equidistant from a fixed point called the focus .

and coordinates of the focus of the upward parabola is: $(h,k+a)$

Where $(h,k)$ is the vertex of the parabola.

Step 3. Explanation

From the given figure of the parabola we have coordinates of the vertex of parabola is (3, 2).

Comparing it with $(h,k)$ we will get,

h = 3 and k = 2 and we have a = 4

So coordinates of the focus of the parabola is

$(h,k+a)$ = (3, 2 + 4) = (3, 6).

Step 4. Conclusion.

Hence, coordinates of the focus of the parabola is (3, 6).