What are the focus and directrix of the parabola with the equation y=1/16x^2

1 answer:

8 0

Y=1/16x^2
multiplying both sides by 16 we get:
16y=x^2
The general form of a parabola is:
(x-h)^2=4p(y-k)
thus
4p=16
p=4
The parabola opens upwrd:
Focus: (h,k-p)
(0,0-4)
=(0,-4)
Directrix: y=-4

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The question is incomplete. The complete question is :

Tests for adverse reactions to a new drug yielded the results given in the table. Drug Placebo headaches No headaches 11 7 91 73 The data will be analyzed to determine if there is sufficient evidence to conclude that an association exists between the treatment (drug or placebo) and the reaction (whether or not headaches were experienced. The results of the test are X2 = 1.798 P-value = .1799. Identify the correct conclusion. O Do not reject the null hypothesis. Report that there insufficient evidence to conclude that treatment and reaction are dependent. O Fail to reject the null hypothesis. Report that there insufficient evidence to conclude that the distribution of headaches is uniform for the drug and placebo. O Reject the null hypothesis. Report that there is sufficient evidence to conclude that treatment and reaction are dependent. O Reject the null hypothesis. Report that there is insufficient evidence to conclude that treatment and reaction are dependent.

Solution :

Given :

Drugs Placebo

Headaches 11 7

No headaches 73 91

The results of the test are :

$X^2=1.798$

The P value is given as = 0.1799

The hypothesis test given for dependent or association between the two variables.

$H_0$ : There is no association between the treatment and the reaction

$H_1$ : There is association between the treatment and the reaction.

If the P value is greater than the alpha value, i.e. when

P value > α (0.05), then we reject the $H_0$ .

Therefore, Do not $\text{reject the null hypothesis}$ . Report that $\text{there insufficient}$ evidence to conclude that $\text{treatment}$ as well as $\text{reaction are dependent}$ .