Write a parabola equation with a focus at (-5,1) and a directrix of y=-5

 is the equation of the parabola

Step-by-step explanation:

Let  be any point on the parabola. Find the distance between and the focus. Then find the distance between and directrix. Equate these two distance equations and the simplified equation in and is equation of the parabola.

The distance between and (2,5) is

The distance between and the directrix, y= -5 is

.

Equate the two distance expressions and square on both sides.

Simplify and bring all terms to one side:

=0

Writing the equation with on one side:

This equation in is true for all other values on the parabola and hence we can rewrite with (x,y) .

So, the equation of the parabola with focus (-5, 1) and directrix is y= -5 is

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

this linear equation would have just one solution.

step-by-step explanation:

the reason why this would have one solution is that it is an expression with just one variable. since that variable is not raised to a power, it will always have just one solution.