Derive the equation of the parabola with a focus at (0, 1) and a directrix of y = −1. (2 points)

Step-by-step explanation:

 Focus =(h,k+p)  

Directrix= y=k-p

Focus given is : (0,1)

And directrix given is : y=-1

(h,k+p) =(0,1)

On comparing the values we get

h=0 and k+p=1

y=k-p= -1

Hence, we gave two equations

k+p=1  and k-p= -1

Substitute p= 1-k in k-p= -1 we get:

k-(1-k) = -1

k-1+k= -1

k=0

Now, we get

h=0 and k=0

And put k=0 in p = 1-k

We get p=1

We have general equation of parabola

Hence, the required equation is :

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

4400

step-by-step explanation: