What is the equation of a parabola with (4,6) as its focus and y = 2 as its directrix

The equation of the parabola is (x - 4)² = 8(y - 4)

Step-by-step explanation:

* Lets revise the equation of a parabola

- If the equation is in the form (x − h)² = 4p(y − k), then:  

• Use the given equation to identify h and k for the vertex, (h , k)

• Use the value of h to determine the axis of symmetry, x = h

• Use h , k and p to find the coordinates of the focus, (h , k + p)  

• Use k and p to find the equation of the directrix, y = k − p

* Now lets solve the problem

∵ The directrix is y = 2

∴ The equation is (x - h)² = 4p(y - k)

∴ The focus is (h , k + p)

∵ The focus is (4 , 6)

∴ h = 4

∵ k + p = 6 ⇒ (1)

∵ The directrix is y = k - p

∴ k - p = 2 ⇒ (2)

* Add (1) and(2) to find k

∴ 2k = 8 ⇒ ÷ 2 for both sides

∴ k = 4

* Substitute the value of k in (1) to find p

∵ 4 + p = 6 ⇒ subtract 4 from both sides

∴ p = 2

* Now lets write the equation

∴ (x - 4)² = 4(2)(y - 4) ⇒ simplify

∴ (x - 4)² = 8(y - 4)

* The equation of the parabola is (x - 4)² = 8(y - 4)

the answer is 31.27mph

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!