Answer:
Attached
Step-by-step explanation:
The conic section you can chose is a parabola
A parabola is a curve where any point on the curve is equidistant from the focus and from a directrix
When you have the vertex and focus points, you can write the equation of the parabola then graph it on a graph tool to visualize the curve.
Assume the vertex is at (3,1) and focus is at (3,5), then you notice here the x-coordinate for vertex and focus is the same , to mean one is top of the other.
This is a regular vertical parabola the x part is squared.
Vertex and focus are 4 units apart. This is by checking the difference in values of y-axis of vertex and focus.This is your p
The equation of the parabola will be
(x-h)²=4p(y-k)
but p=4
(x-3)²=4(4)(y-1)
(x-3)²=16(y-1)
x²-6x+9=16y-16
x²-6x-16y+25=0-----------------equation of the parabola
It is a right-side up parabola
