Aparabola and its focus are shown on the graph. the vertex of the parabola is at (0,0).

what is the equation of the directrix of the parabola?

y = 3
y = –3
x = 3
x = –3

x= -3

Step-by-step explanation:

A parabola is set of all points in a plane which are an equal distance away from a given point and given line. The point is called the focus of the parabola, and the line is called the directrix .

The directrix is perpendicular to the axis of symmetry of a parabola and does not touch the parabola. If the axis of symmetry of a parabola is vertical, the directrix is a horizontal line .

focus of parabola=(3,0)

(y - k)² = 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - p.

Here, equation of parabola is:

y²=12x i.e. p=3,h=0

(since, focus is (3,0) i.e. k=0 and h+p=3 also at x=0 y=0 which will be true if h=0)

Hence, directrix is x= -3

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step-by-step explanation:

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hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)