Answer the following and give a step-by-step explanation for the solution of each.

Question

I. Find the vertex, axis of symmetry, focus and directrix of the parabola represented by the given equation. Discuss the process/steps as to how you got the values.

(y - 3)^2 = 3/4 (x - 4)

II. Find the equation of the parabola described. Find the two points that define the latus rectum. Explain the solutions completely.

1. with focus at (-5, 0); vertex at (0, 0)

2. with vertex at (-6, 3); focus at (0, 3)

Answer 1

I. Vertex at (4, 3); 4p = 3/4 p = 3/16; axis of symmetry y = 3,Focus at point (4 + 3/16, 3) = (67/16, 3);

diretrix x = 4 - 3/16 = 61/16.

II. 1. p = - 5 y² = - 20x

2.p = 0 + 6 = 6; (y - 3)² = 24(x + 6)