1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Contact [7]
3 years ago
15

If the vertices of an ellipse are at (1, 5) and (1, -5) and (3, 0) is a point on the ellipse, what is the ellipse equation?

Mathematics
2 answers:
AleksandrR [38]3 years ago
6 0

Answer:

\dfrac{(x-1)^2}{4}+\dfrac{y^2}{25}=1

Step-by-step explanation:

The equation of the ellipse is

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

where (x_0,y_0) are the coordinates of the center.

If the vertices of an ellipse are at A(1, 5) and B(1, -5), then the center is the midpoint of the segment AB. Hence, the center has coordinates

\left(\dfrac{1+1}{2},\dfrac{5+(-5)}{2}\right)=(1,0).

The coordinates of the vertices satisfy the equation:

\dfrac{(1-1)^2}{a^2}+\dfrac{(5-0)^2}{b^2}=1\Rightarrow b^2=25.

If (3, 0) is a point on the ellipse, then its coordinates satisfy the equation:

\dfrac{(3-1)^2}{a^2}+\dfrac{(0-0)^2}{b^2}=1\Rightarrow a^2=4.

Therefore, the equation of the ellipse is

\dfrac{(x-1)^2}{4}+\dfrac{y^2}{25}=1.


Ad libitum [116K]3 years ago
5 0

Answer:

the answer is b.

Step-by-step explanation:

You might be interested in
PLEASE HELP WILL MARK BRAINLIEST
egoroff_w [7]
Option 4 is the correct answer
3 0
3 years ago
Read 2 more answers
Write the number that is 1 more than 8,325
borishaifa [10]
The answer is to this question is 8,326
3 0
3 years ago
Read 2 more answers
Explain why it works to break apart a number by place values to multiply
IrinaK [193]
Idononoooont know boi
3 0
3 years ago
Read 2 more answers
A livestock pen is built in the shape of a rectangle that is 2 times as long as it is wide. the perimeter is 42 feet. if the mat
Lorico [155]
Let width = x ft  then 
2x + 2(2x) = 42
6x = 42
x = 7 

so the width is 7 ft and length is 14 ft.

So the cost to build the pen =  14*1.25 + 14*1,25 + 7*2.50 + 7*2.50
=  70  answer
4 0
3 years ago
If PQRS is a square and TR = 17, find each missing value. Round to the nearest tenth.
mestny [16]

<h3>\huge\mathfrak\pink{Answer}</h3><h3>The area of rhombus PQRS is 120 m. </h3>

Step-by-step explanation:

<h3>correct me if I'm wrong.</h3>

\huge\mathfrak\red{Hope it's help}

8 0
2 years ago
Other questions:
  • Find 631.44 * 6.314 and round your answer to the nearest thousandth.
    10·1 answer
  • Is each expression algebraic or numerical<br> a. 7/2 <br> b. 4m + 6 <br> c. 2(5 - 4)
    10·1 answer
  • Which prism has 12 vertices?<br><br> rectangular<br> pentagonal<br> hexagonal<br> octagonal
    8·2 answers
  • Given x is less than y compare the following expressions and determine which is greater 2 x - y or 2y - x explain your answer
    6·1 answer
  • Can someone help me?
    8·2 answers
  • Find the output, k, when the input, t, is 3.<br> k = 13t – 2<br> k=
    8·2 answers
  • The measure of angle 3 is 42°. What is the measure of angle 1 in degrees?
    15·1 answer
  • Find the equation of the ellipse with the following properties. The ellipse with foci at (0, 6) and (0, -6); y-intercepts (0, 8)
    9·1 answer
  • A baker used 2/3 cup of flour to make 1/3 of a recipe. How much flower would the baker use to make the whole recipe?
    6·1 answer
  • What represents the quantitative forecast
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!