Is it true a parabola’s Cruises it’s focus?
Also in a hyperbola, is the distance between the foci always larger than the length of the transverse axis?
I have no idea what a parabola's "Cruises" is.
(b) yes.
for many further details, google "parabola" or "hyperbola"
Yes, it is true that a parabola "cruises" through its focus. However, to understand this concept, let me explain how a parabola is defined and how it relates to its focus.
A parabola is a U-shaped curve defined by a quadratic equation of the form y = ax^2 + bx + c. The key defining feature of a parabola is that it is symmetrical and has a focus.
The focus of a parabola is a point that lies on the axis of symmetry, which is a line that cuts the parabola into two equal halves. The focus is equidistant from the vertex (the lowest point of the parabola) and the directrix (a line located above the vertex).
To determine the location of the focus, you need to know the equation of the parabola in standard form (y = ax^2 + bx + c). The coordinates of the focus can be found using the formula:
Focus coordinates = (h, k + (1/4a))
Here, (h, k) represents the vertex of the parabola, and 'a' is the coefficient of the x^2 term in the equation.
In summary, a parabola does indeed pass through its focus. The focus is an important feature of a parabola as it helps define its shape and characteristics.