What is the equation of the parabola with vertex (3, 4) and focus (6, 4).

Solution:

Given, the vertex = (3, 4)

Focus = (6, 4)

We have to find the equation of the parabola.

Since the vertex and the focus lie on the same horizontal line y = 4.

The equation of the parabola in vertex form is given by

(x - h) = a(y - k)²

Here, h = 3, k = 4

x - 3 = a(y - 4)²

x = a(y - 4)² + 3

The focus of the parabola is at (3 + (1/4a), 4)

So, 3 + 1/4a = 6

1/4a = 6 - 3

1/4a = 3

1/4 = 3a

a = 1/12

Put the value of a in vertex form,

x = (1/12)(y - 4)² + 3

Therefore, the equation of the parabola is x = (1/12)(y - 4)² + 3

What is the equation of the parabola with vertex (3, 4) and focus (6, 4).

Summary:

The equation of the parabola with vertex (3, 4) and focus (6, 4) is x = (1/12)(y - 4)² + 3.