Question

HELP! ONLY IF YOU KNOW THE ANSWER

also this goes with the other question I asked
Write the standard equation of the conic section you chose with its center or vertex at the origin. Describe the graph.

Answer 1

I only know question number one; the answer is

A parabola is a curve where any point on the curve is equidistant from the focus and from a directrix.

Explanation:

Answer 2

Attached

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