Final answer:
To write the equation of a parabola given the vertex and focus, use the formula (x - h)² = 4p (y - k), where (h, k) is the vertex and (h + p, k) is the focus. Substitute the given vertex and focus values into the formula and solve for p. Then substitute the value of p back into the equation.
Step-by-step explanation:
To write the equation of a parabola given the vertex and focus, we can use the formula: (x - h)² = 4p (y - k), where (h, k) is the vertex and (h + p, k) is the focus.
Using the given vertex (3, 6) and focus (6, 6), we can substitute the values into the formula and solve for p:
(x - 3)² = 4p (y - 6)
Substituting the x-coordinate of the focus into the equation, we get:
(6 - 3)² = 4p (6 - 6)
Simplifying further, we have:
9 = 4p
Dividing both sides by 4, we find:
p = 9/4
Now, substituting the value of p back into the equation, we get the equation of the parabola:
(x - 3)² = 9/4 (y - 6)