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The foci of the ellipse 25 (x + 1)2 + 9(y + 2)2 = 225 are at:
- a)(–2, 1) and (–2, 6)
- b)(–1, 2) and (–1, –6)
- c)(–1, –2) and (–1, –6)
- d)(–1, –2) and (–2, –1)
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The foci of the ellipse 25 (x + 1)2+ 9(y + 2)2= 225 are at:a)(–2...
Here equation of ellipse is 25(x + 1)2 + 9(y + 2)2 = 225
0r (x + 1)2/9 + (y + 2)2/25 = 1
Centre of the ellipse is (–1,–2)
a2 = 9, b2 = 25
a = 3, b = 5
e = (1-a2/b2)1/2
e = (1-9/25)1/2
e = +-4/5
be = +-4
Foci : (-1,-6)(-1,2)
0r (x + 1)2/9 + (y + 2)2/25 = 1
Centre of the ellipse is (–1,–2)
a2 = 9, b2 = 25
a = 3, b = 5
e = (1-a2/b2)1/2
e = (1-9/25)1/2
e = +-4/5
be = +-4
Foci : (-1,-6)(-1,2)
Most Upvoted Answer
The foci of the ellipse 25 (x + 1)2+ 9(y + 2)2= 225 are at:a)(–2...
Here equation of ellipse is 25(x + 1)2 + 9(y + 2)2 = 225
0r (x + 1)2/9 + (y + 2)2/25 = 1
Centre of the ellipse is (–1,–2)
a2 = 9, b2 = 25
a = 3, b = 5
e = (1-a2/b2)1/2
e = (1-9/25)1/2
e = +-4/5
be = +-4
Foci : (-1,-6)(-1,2)
0r (x + 1)2/9 + (y + 2)2/25 = 1
Centre of the ellipse is (–1,–2)
a2 = 9, b2 = 25
a = 3, b = 5
e = (1-a2/b2)1/2
e = (1-9/25)1/2
e = +-4/5
be = +-4
Foci : (-1,-6)(-1,2)
Community Answer
The foci of the ellipse 25 (x + 1)2+ 9(y + 2)2= 225 are at:a)(–2...
Given:
The equation of the ellipse is 25(x-1)^2 + 9(y-2)^2 = 225.
To find:
The foci of the ellipse.
Solution:
Step 1: Identify the standard form of the ellipse equation.
The given equation is in the standard form of an ellipse:
((x-h)^2)/a^2 + ((y-k)^2)/b^2 = 1,
where (h,k) represents the center of the ellipse.
Step 2: Rewrite the given equation in the standard form.
25(x-1)^2 + 9(y-2)^2 = 225
Dividing both sides by 225, we get:
((x-1)^2)/9 + ((y-2)^2)/25 = 1
Comparing this equation with the standard form, we can see that:
a^2 = 9, which means a = 3,
b^2 = 25, which means b = 5.
Step 3: Find the coordinates of the center.
From the given equation, we can see that the center of the ellipse is at (1, 2).
Step 4: Find the coordinates of the foci.
The distance from the center to each focus is given by c, where c^2 = a^2 - b^2.
Plugging in the values of a and b, we have:
c^2 = 9 - 25 = -16
Since c^2 is negative, it means that the ellipse is a vertically elongated ellipse. The foci lie on the major axis, which is the y-axis.
The coordinates of the foci are (h, k + c) and (h, k - c).
Plugging in the values of h, k, and c, we have:
F1: (1, 2 + 4) = (1, 6)
F2: (1, 2 - 4) = (1, -2)
Step 5: Final Answer
The foci of the ellipse are at (1, 6) and (1, -2).
Therefore, the correct answer is option 'B': (1, 2) and (1, 6).
The equation of the ellipse is 25(x-1)^2 + 9(y-2)^2 = 225.
To find:
The foci of the ellipse.
Solution:
Step 1: Identify the standard form of the ellipse equation.
The given equation is in the standard form of an ellipse:
((x-h)^2)/a^2 + ((y-k)^2)/b^2 = 1,
where (h,k) represents the center of the ellipse.
Step 2: Rewrite the given equation in the standard form.
25(x-1)^2 + 9(y-2)^2 = 225
Dividing both sides by 225, we get:
((x-1)^2)/9 + ((y-2)^2)/25 = 1
Comparing this equation with the standard form, we can see that:
a^2 = 9, which means a = 3,
b^2 = 25, which means b = 5.
Step 3: Find the coordinates of the center.
From the given equation, we can see that the center of the ellipse is at (1, 2).
Step 4: Find the coordinates of the foci.
The distance from the center to each focus is given by c, where c^2 = a^2 - b^2.
Plugging in the values of a and b, we have:
c^2 = 9 - 25 = -16
Since c^2 is negative, it means that the ellipse is a vertically elongated ellipse. The foci lie on the major axis, which is the y-axis.
The coordinates of the foci are (h, k + c) and (h, k - c).
Plugging in the values of h, k, and c, we have:
F1: (1, 2 + 4) = (1, 6)
F2: (1, 2 - 4) = (1, -2)
Step 5: Final Answer
The foci of the ellipse are at (1, 6) and (1, -2).
Therefore, the correct answer is option 'B': (1, 2) and (1, 6).
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Question Description
The foci of the ellipse 25 (x + 1)2+ 9(y + 2)2= 225 are at:a)(–2, 1) and (–2, 6)b)(–1, 2) and (–1, –6)c)(–1, –2) and (–1, –6)d)(–1, –2) and (–2, –1)Correct answer is option 'B'. Can you explain this answer? for JEE 2026 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The foci of the ellipse 25 (x + 1)2+ 9(y + 2)2= 225 are at:a)(–2, 1) and (–2, 6)b)(–1, 2) and (–1, –6)c)(–1, –2) and (–1, –6)d)(–1, –2) and (–2, –1)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The foci of the ellipse 25 (x + 1)2+ 9(y + 2)2= 225 are at:a)(–2, 1) and (–2, 6)b)(–1, 2) and (–1, –6)c)(–1, –2) and (–1, –6)d)(–1, –2) and (–2, –1)Correct answer is option 'B'. Can you explain this answer?.
The foci of the ellipse 25 (x + 1)2+ 9(y + 2)2= 225 are at:a)(–2, 1) and (–2, 6)b)(–1, 2) and (–1, –6)c)(–1, –2) and (–1, –6)d)(–1, –2) and (–2, –1)Correct answer is option 'B'. Can you explain this answer? for JEE 2026 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The foci of the ellipse 25 (x + 1)2+ 9(y + 2)2= 225 are at:a)(–2, 1) and (–2, 6)b)(–1, 2) and (–1, –6)c)(–1, –2) and (–1, –6)d)(–1, –2) and (–2, –1)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The foci of the ellipse 25 (x + 1)2+ 9(y + 2)2= 225 are at:a)(–2, 1) and (–2, 6)b)(–1, 2) and (–1, –6)c)(–1, –2) and (–1, –6)d)(–1, –2) and (–2, –1)Correct answer is option 'B'. Can you explain this answer?.
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