Conics Parabolas

What is the relationship between the focus and the directrix?

• The distance from any point on the parabola to the focus is equal to the distance from that point to the directrix.

• The focus is always located at the vertex of the parabola.

• The directrix is a line that is always above the parabola.

• The focus and directrix are two points that define the width of the parabola.

What is the difference between a vertical and horizontal parabola?

• A vertical parabola opens left or right and has the form (y-k)² = 4p(x-h), while a horizontal parabola opens up or down and has the form (x-h)² = 4p(y-k).

• A vertical parabola opens up or down and has the form (x-h)² = 4p(y-k), while a horizontal parabola opens left or right and has the form (y-k)² = 4p(x-h).

• Both vertical and horizontal parabolas open in the same direction and have the same form.

• A vertical parabola opens down and has the form (x-h)² = 4p(y-k), while a horizontal parabola opens up and has the form (y-k)² = 4p(x-h).

How can you identify a parabola from its equation?

• A parabola can be identified by the presence of a squared term and a linear term, typically in the form y = ax² + bx + c or x = ay² + by + c.

• A parabola is identified by having only linear terms in its equation.

• A parabola can be identified by the presence of a cubic term in its equation.

• A parabola is identified by having no squared terms in its equation.

What is the effect of changing the value of 'h' and 'k' in the standard form of a parabola?

• It changes the width of the parabola.

• It shifts the parabola horizontally and vertically, respectively, without altering its shape.

• It reflects the parabola across the x-axis.

• It rotates the parabola around the origin.

How do you determine the direction a parabola opens?

• If the coefficient of the squared term is positive, the parabola opens upwards; if negative, it opens downwards.

• If the coefficient of the squared term is zero, the parabola is horizontal.

• If the coefficient of the squared term is positive, the parabola opens downwards; if negative, it opens upwards.

• The direction of the parabola is determined by the linear term's coefficient.

What is a parabola?

• A symmetrical, U-shaped curve defined as the set of all points equidistant from a fixed point (the focus) and a fixed line (the directrix).

• A circular shape that represents the path of an object in motion under the influence of gravity.

• A straight line that intersects a curve at two points.

• A three-dimensional shape that has a constant width and height.

How do you find the coordinates of the focus from the equation (y-k)² = 4p(x-h)?

• The focus is located at (h+p, k) for a right-opening parabola and (h-p, k) for a left-opening parabola.

• The focus is located at (h, k+p) for a right-opening parabola and (h, k-p) for a left-opening parabola.

• The focus is located at (h, k) for both right-opening and left-opening parabolas.

• The focus is located at (h+2p, k) for a right-opening parabola and (h-2p, k) for a left-opening parabola.

What is the vertex of a parabola?

• The point where the parabola intersects the x-axis.

• The highest or lowest point of the parabola, depending on its orientation.

• The distance between the focus and the directrix.

• The axis of symmetry of the parabola.

What is the standard form of a vertical parabola?

• (x-h)² = 4p(y-k)

• (y-k)² = 4p(x-h)

• (x-h)² = 4p(y+k)

• (y+k)² = 4p(x-h)

What does the value of 'p' represent in a parabola?

• The distance from the vertex to the focus and the distance from the vertex to the directrix.

• The length of the parabola's axis of symmetry.

• The width of the parabola at its vertex.

• The distance between the two foci of the parabola.