Find the standard form of the equation of the parabola with a focus at (0, -8) and a directrix at y = 8.

The standard form of the equation of the parabola is .

Step-by-step explanation:

The general form of a parabola is

Where, (h,k) is vertex, (h,k+p) is focus and y=k-p is directrix.

Focus of the parabola is (0, -8).

       .... (1)

Directrix of the parabola is

          .... (2)

On adding (1) and (2) we get

Put this value in equation (1).

The value of p is -8.

Substituent h=0,k=0 and p=-8 in general form of parabola.

Divide both sides by -32.

Therefore the standard form of the equation of the parabola is .

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step-by-step explanation:

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).