Aparabola has a vertex at (0,0). the focus of the parabola is located at (4,0). what is the equation of the directrix?

The equation of parabola is given by:

where,

(h, k) is the vertex.

Focus = (h+a, k)

As per the statement:

A parabola has a vertex at (0,0).

⇒

The focus of the parabola is located at (4,0).

⇒

⇒

⇒a = 4

then, equation become:

We have to find the equation of directrix

The equation of directrix is, x = h-a

then;

x = 0-4 = -4

⇒x = -4

Therefore, the equation of directrix is, x = -4

5=812a+9+3

step 1: simplify both sides of the equation.

5=812a+9+3

5=(812a)+(9+3)(combine like terms)

5=812a+12

5=812a+12

step 2: flip the equation.

812a+12=5

step 3: subtract 12 from both sides.

812a+12−12=5−12

812a=−7

step 4: divide both sides by 812.

812a /812 = -7/812

a= -1/116

so the answer is

a=   -1/116