In the general case in Cartesian coordinates, you would use the definition of a parabola as the locus of points equidistant from the focus and directrix. The equation would equate the square of the distance from a general point (x, y) to the focus with the square of the distance from that point to the directrix line.
Suppose the focus is located at (h, k) and the equation of the directrix is ax+by+c=0. The expression for the square of the distance from (x, y) to the point (h, k) is ...
(d₁)² = (x-h)²+(y-k)²
The expression for the square of the distance from (x, y) to the directrix line is
(d₂)² = (ax+by+c)²/(a²+b²)
Equating these expressions gives the equation of the parabola.
(x-h)²+(y-k)² = (ax+by+c)²/(a²+b²)
When the directrix is parallel with one of the axes, one of the coefficents "a" or "b" is zero and the equation becomes much simpler. Often, it would be easier to make use of the formula (for a directrix parallel to the x-axis):
y = 1/(4p)*(x -h)² +k
where the (h, k) here is the vertex, the point halfway between the focus and directrix, and "p" is the (signed) distance from the focus to the vertex. (p is positive when the focus is above or to the right of the vertex.)
Complete question :
En un concesionario de coches hay modelos de varios colores. Los rojos suponen 1/6 del total, los azules, 2/9 del total, y los blancos, 4/15 del total.
a)¿Cuál de esos colores es el más frecuente?
b) Si hay 40 coches azules, ¿cuántos hay en total?
Responder:
Coches blancos
180 coches
Explicación paso a paso:
Dado que:
Rojo = 1/6 del total
Azul = 2/9 del total
Blanco = 4/15 del total
Para determinar qué color es el más alto, convierta los valores en decimal:
1/6 = 0,166667
2/9 = 0,2222
15/4 = 0,26667
Por lo tanto;
4/15> 2/9> 1/6
Por tanto, los coches blancos son los que más
2.)
Sea Número total = x
Por lo tanto,
2/9 de x = 40
2x / 9 = 40
2x = 360
x = 180
Por tanto, hay 180 coches en total.
