Write the standard form of the conic equation in which Eccentricity = sqr(11)/4

Vertices: (0, 9+4(sqr 5)), (0, 9-4(sqr(5))

I have the answer of x^2 /25 + (y-9)^2 /80 = 1 but I don't understand how to get it. Thank you so much.

Write the standard form of the conic equation in which Eccentricity = sqr(11)/4

Vertices: (0, 9+4(sqr 5)), (0, 9-4(sqr(5))

I have the answer of x^2 /25 + (y-9)^2 /80 = 1 but I don't understand how to get it. Thank you so much.

Tutors, please sign in to answer this question.

San Diego, CA

Eccentricity= c/a=sqrt(11)/4

As per given vertices,major axis is vertical.

9+4sqrt(5)-9+4sqrt(5)=8sqrt(5)=2a

So, a=4sqrt(5)

c/a=sqrt(11)/4. =c/4sqrt(5)

c=sqrt(55)

c^2= a^2. -b^2

55=80-b^2

b=5

Center coordinates= (0,9)

Equation of ellipse is

[(x^2)/25] + [(y-9)^2]/80=1

YOU are welcome to revert back if any step is not clear.

Tyler L.

Patient and Knowledgeable Math/Science Tutor

New York, NY

4.9
(28 ratings)

Terri M.

Test Prep Specialist with 2400 SAT, 35 ACT, 770 GMAT, and 177 LSAT

New York, NY

5.0
(220 ratings)

Juan R.

Algebra, Trig, Calculus, and College Math

Forest Hills, NY

5.0
(75 ratings)

- Calculus 1940
- Calculus 1 393
- Pre Calculus 343
- Algebra 2 3068
- Calculus 2 296
- Math 8245
- Math Help 4708
- Word Problem 4544
- Algebra 4457
- Algebra 1 3607