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4 years ago

At which points are the tangents drawn to the ellipse x 2 + y 2 = [ a ] x + [ a ] y parallel to

Mathematics

1 answer:

In-s [12.5K]4 years ago

3 0

The given equation of the ellipse is x^2 + y^2 = 2 x + 2 y

At tangent line, the point is horizontal with the x-axis therefore slope = dy / dx = 0

<span>So we have to take the 1st derivative of the equation then equate dy / dx to zero.</span>

x^2 + y^2 = 2 x + 2 y

x^2 – 2 x = 2 y – y^2

(2x – 2) dx = (2 – 2y) dy

(2x – 2) / (2 – 2y) = 0

2x – 2 = 0

x = 1

To find for y, we go back to the original equation then substitute the value of x.

x^2 + y^2 = 2 x + 2 y

1^2 + y^2 = 2 * 1 + 2 y

y^2 – 2y + 1 – 2 = 0

y^2 – 2y – 1 = 0

Finding the roots using the quadratic formula:

y = [-(- 2) ± sqrt ( (-2)^2 – 4*1*-1)] / 2*1

y = 1 ± 2.828

y = -1.828 , 3.828

<span>Therefore the tangents are parallel to the x-axis at points (1, -1.828) and (1, 3.828).</span>

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What is the 15% service tip on a $25.50 dinner in a restraunt

adell [148]

Basically you do 25.50 time .15 (15% is equal to .15) and you get 3.825 or $3.83

hope this helped

8 0

3 years ago

Select True or False for each statement. 1 4 9 + 7 6 9 is equal to 8 1 9 . 5 5 6 + 3 3 6 is equal to 8 2 6 . 4 5 8 − 2 4 8 is eq

Elena L [17]

Answer:

(1) False

(2) False

(3). False

(4) False

Step-by-step explanation:

According to the problem, calculation of the given data are as follows,

(1). Given, 149 + 769 = 819

By calculating 149 + 769 = 918

Hence, False

(2). Given, 556 + 336 = 826

By calculating 556 + 336 = 892

Hence, False

(3). Given, 458 - 248 = 238

By calculating 458 - 248 = 210

Hence, False

(4). Given, 658 - 228 = 438

By calculating 658 - 228 = 430

Hence, False

4 0

3 years ago

If 8x=7, what is the value of 5 (x+1/2)

beks73 [17]

X=7/8
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5 0

3 years ago

All cars can be classified into one of four groups: the subcompact, the compact, the midsize, and the full-size. There are

Olegator [25]

Answer:

p value = 0.302

Step-by-step explanation:

Given that all cars can be classified into one of four groups: the subcompact, the compact, the midsize, and the full-size. There are five cars in each group. Head injury data (in hic) for the dummies in the driver's seat are listed below.

H_0: All cars have same mean values

H_a: atleast two cars have different mean values

(Two tailed anova test)

Anova: Single Factor

SUMMARY

Groups Count Sum Average Variance

Subcompact 5 3444 688.8 48502.7

compact 5 2879 575.8 4582.7

Midsize 5 2534 506.8 18720.2

Full size 5 2689 537.8 23905.2

ANOVA

Source of Variation SS df MS F P-value F crit

Between Groups 94825 3 31608.33 1.321 0.302 3.24

Within Groups 382843.2 16 23927.7

Total 477668.2 19

Since p value of 0.302 is greater than 0.05 significance level we accept null hypothesis.

p value = 0.302

6 0

3 years ago

A small radio transmitter broadcasts in a 53 mile radius. If you drive along a straight line from a city 70 miles north of the t

son4ous [18]

Answer:

29% of the drive

Step-by-step explanation:

The plot of the problem is:

Transmitter at origin (0,0)

City to the north at (0,70)

City to the east at (74,0)

The path from city to city is a line with slope:

m = (-70)/74 = -35/37

and y-intercept at y = 70, so the equation is y = (-35/37)*x + 70.

The transmitter reach the area enclosed by the next circle:

x^2 + y^2 = 53^2

See the picture attached

The intersection is gotten from the picture or solving:

x^2 + [(-35/37)*x + 70]^2 = 53^2

the points approximately are: (24.1, 47.2) and (45.8, 26.7)

From Pythagorean theorem the total distance of the trip is:

d1 = √(70^2 + 74^2) ≈ 101.9 miles

And the distance when the signal is picked up is:

d2 =√ [(45.8 - 24.1)^2 + (47.2 - 26.7)^2] ≈ 29.9 miles

You will pick up a signal from the transmitter in (d2/d1)*100 = 29% of the drive.

4 0

4 years ago