a parabola can be drawn given a focus of (-8,-1) and a directrix of x=10. write the equation of the parabola in any form

(x - 8)² = 20(y + 6)

Step-by-step explanation:

The focus of the parabola is (8,-1) and the equation of the directrix is y = - 11.

So, the parabola opens up and the axis of symmetry is x = 8 line.

Now, the axis of symmetry and the directrix meet at the point (8,-11).

So, the vertex of the parabola will be the midpoint of (8,-1) and (8,-11) i.e. (8,-6).

Now, half of the distance between the focus and the directrix is = a =  units.

So, the equation of the parabola in vertex form will be

(x - 8)² = 4 × 5 × (y + 6)

⇒ (x - 8)² = 20(y + 6) (Answer)

Step-by-step explanation:

for a it would be 24 children.

for b i don't understand the question. is it saying for each individual person they pick 5 reds to 7 greens or is it the whole group. clarify and i hope this can you.

step-by-step explanation:

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .