Write the equation for a parabola with a focus at (-4,3) and a directrix at y = 5.

Y=?

The equation for a parabola with a focus at (-4, 3) and a directrix at y = 5 is; y = ¹/₄(x + 4)² + 4

The standard form of the equation of a parabola is given by;

(x - h)² = 4p(y - k)

where;

We are given the coordinates of the focus of the parabola as (-4, 3)

Thus, from (h, k + p)

h = -4

k + p = 3   (eq 1)

From y = k - p,  since it has a directrix of y = 5, then;

k - p = 5   (eq 2)

→ Add equations (1) to (2) to get;

2k = 8

k = 8/2

k = 4

Put 4 for k in equation (1) to get

4 + p = 3

p = 4 - 3

p = 1

Plugging in the relevant values into the standard form of the equation of the parabola gives (x - h)² = 4p(y - k)

(x - (-4))² = 4(1)(y - 4)

⇒ (x + 4)² = 4(y - 4)

⇒ y = ¹/₄(x + 4)² + 4

The equation of the parabola is y = ¹/₄(x + 4)² + 4

Read more about equation of parabola at; link

7! = 7×6×5×4×3×2

3! = 3× 2

as 7! is multiple of 3! because 7! contains 3! that is 3× 2 as factor

so 7! /(3! ) = 7× 6× 5× 4

= 42 × 20

= 840

its b) 840✌✌✌

dhruv⭐