Match the steps to find the equation of the parabola with focus (-1,2) and directrix x=5

Mathematics

1 answer:

Paha777 [63]2 years ago

4 0

Given that parabola has a focus of (-1,2) and directrix of x=5, Matching the steps with the equations we shall have:
1. Use (x,y)⇒choose a point from the parabola.

2. √[(x+1)²+(y-2)²]⇒Find the distance from the focus to the point on the parabola

3. √(x-5)²⇒Find the distance from the point on the parabola to the directrix

4. √[(x+1)²+(y-2)²]=√(x-5)²⇒Set the distance from focus to the point equal to the distance from directrix to the point

5. (x+2)²+(y-2)²=(x-5)² ⇒Square both sides and simplify
y²-4y+4=-12x+24

6. x=-y²/12+y/3+5/3⇒Write the equation of the parabola

You might be interested in

What is 1x1= 3y128367138 riding it equals to 1

Anon25 [30]

Yes that is extremely accurate

5 0

2 years ago

Read 2 more answers

Find the amount of sap the maple syrup producer collected from each tree if the total amount (5 gallons) was redistributed equal

Afina-wow [57]

The picture in the attached figure

we know that
total amount of sap =[3*(1/4)+2*(3/8)+4*(5/8)+1*(1)]
total amount of sap =[(3/4)+(6/8)+(20/8)+(1)]
total amount of sap =[(3/4)+(3/4)+(10/4)+(4/4)]
total amount of sap =[20/4]
total amount of sap =5 gallons
total of trees=10

<span>[amount of sap collected from each tree]=total amount of sap/total of trees
</span>
[amount of sap collected from each tree]=5/10----> 0.5 gallons per tree

the answer is
0.5 gallons

7 0

2 years ago

Read 2 more answers

In a recent study of 42 eighth graders, the mean number of hours per week that they watched television was 19.6. Assume the popu

olya-2409 [2.1K]

Answer:

$19.6-2.42\frac{5.8}{\sqrt{42}}=17.43$

$19.6+2.42\frac{5.8}{\sqrt{42}}=21.77$

And the best option for this case would be:

a. (17.5, 21.7)

Step-by-step explanation:

Information given

$\bar X= 19.6$ represent the sample mean

$\mu$ population mean

$\sigma= 5.8$ represent the population deviation

n=42 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

The degrees of freedom, given by:

$df=n-1=42-1=41$

Since the Confidence is 0.98 or 98%, the significance would be $\alpha=0.02$ and $\alpha/2 =0.1$ , and the critical value would be $t_{\alpha/2}=2.42$