Mathematics, 05.11.2019 05:31, BradFarquharson472

An ellipse has a center of (3, 1), a focus of (8, 1), and a directrix of x = 36.8. which is the equation of the ellipse?

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answered: fonsworth5

The equation of the ellipse is $\frac{(x-3)^2}{169} +\frac{(y-1)^2}{144}=1$

Step-by-step explanation:

The equation of the ellipse is given by:

$\frac{(x-x_0)^2}{a^2} +\frac{(y-y_0)^2}{b^2}=1$

where:

Center of the ellipse is (x₀,y₀)

Vertices: (x₀±a,y₀)

c: distance from the center to the focus $c=\sqrt{a^2-b^2}$

Eccentricity $e=\frac{c}{a}$

Directrix= $x_0 + \frac{a^2}{c}$

So we can obtain the values:

c=(8, 1)-(3, 1)=8-3= (5,0)=5

x₀= 3

y₀= 1

The directrix is x = 36.8

$36.8 = x_0 + \frac{a^2}{c}\\ 36.8 = 3 + \frac{a^2}{5}\\ 36.8 -3= \frac{a^2}{5}\\ 33.8\times 5= a^2\\ 169=a^2\\ \sqrt{169} =a\\ a=13$

Then, we have to obtain b:

$c=\sqrt{a^2-b^2}\\ c^2=a^2-b^2\\ b^2=a^2-c^2\\ b^2=13^2-5^2\\ b^2=169-25\\ b=\sqrt{144} \\ b=12$

The equation of the ellipse is:

$\frac{(x-3)^2}{13^2} +\frac{(y-1)^2}{12^2}=1 \\ \frac{(x-3)^2}{169} +\frac{(y-1)^2}{144}=1$

answered: hanz73

the first option is correct

Step-by-step explanation:

answered: Guest

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

the function given is y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 = -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

answered: Guest

i think 5 miles per hour

step-by-step explanation: