How to write the equation of a parabola when given a point that passes through as well

The video tutorial explains how to write the equation of an ellipse when given a vertex, a point, and the axis of symmetry. It starts by identifying the axis of symmetry and determining the direction in which the parabola opens. The instructor then uses the parabola equation to find the vertex and solve for the variable P by plotting points. Finally, the video demonstrates how to calculate P and finalize the equation, ensuring the parabola opens in the correct direction.

What is the general form of the equation for an ellipse when given a vertex and a point?

Explain how to substitute the vertex coordinates into the equation of the ellipse.

What steps are involved in finding the value of P in the equation of the ellipse?

How do you determine the direction in which the parabola opens based on the axis of symmetry?

What is the significance of the focus in the context of the parabola's equation?