GMAT Exam > GMAT Questions > On the coordinate plane, each point lying on ...
Start Learning for Free
On the coordinate plane, each point lying on a circle has its x and y coordinates greater than or equal to zero. If the centre of the circle lies at (3,4), what is the maximum possible area of the circle?
- a)6π
- b)8π
- c)9π
- d)12π
- e)16π
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
On the coordinate plane, each point lying on a circle has its x and y ...
The maximum possible area of a circle occurs when the circle has the maximum possible radius. In this case, the maximum possible radius occurs when a point on the circle is located on the x-axis or the y-axis.
If a point on the circle is located on the x-axis, its coordinates would be (r, 0) where r is the radius of the circle. Similarly, if a point on the circle is located on the y-axis, its coordinates would be (0, r) where r is the radius of the circle.
Using the distance formula, we can calculate the distance between the center of the circle (3, 4) and a point on the x-axis (r, 0) or the y-axis (0, r):
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
For the x-axis:
Distance = √((r - 3)^2 + (0 - 4)^2)
= √((r - 3)^2 + 16)
= √(r^2 - 6r + 9 + 16)
= √(r^2 - 6r + 25)
For the y-axis:
Distance = √((0 - 3)^2 + (r - 4)^2)
= √(9 + (r - 4)^2)
= √(r^2 - 8r + 16 + 9)
= √(r^2 - 8r + 25)
Since the radius of the circle cannot be negative, we can set the distances equal to zero and solve for r:
√(r^2 - 6r + 25) = 0
r^2 - 6r + 25 = 0
(r - 5)(r - 5) = 0
r = 5
So, the maximum possible radius of the circle is 5.
The maximum possible area of the circle is given by the formula: A = πr^2
A = π(5^2)
A = 25π
Therefore, the maximum possible area of the circle is 25π units squared.
If a point on the circle is located on the x-axis, its coordinates would be (r, 0) where r is the radius of the circle. Similarly, if a point on the circle is located on the y-axis, its coordinates would be (0, r) where r is the radius of the circle.
Using the distance formula, we can calculate the distance between the center of the circle (3, 4) and a point on the x-axis (r, 0) or the y-axis (0, r):
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
For the x-axis:
Distance = √((r - 3)^2 + (0 - 4)^2)
= √((r - 3)^2 + 16)
= √(r^2 - 6r + 9 + 16)
= √(r^2 - 6r + 25)
For the y-axis:
Distance = √((0 - 3)^2 + (r - 4)^2)
= √(9 + (r - 4)^2)
= √(r^2 - 8r + 16 + 9)
= √(r^2 - 8r + 25)
Since the radius of the circle cannot be negative, we can set the distances equal to zero and solve for r:
√(r^2 - 6r + 25) = 0
r^2 - 6r + 25 = 0
(r - 5)(r - 5) = 0
r = 5
So, the maximum possible radius of the circle is 5.
The maximum possible area of the circle is given by the formula: A = πr^2
A = π(5^2)
A = 25π
Therefore, the maximum possible area of the circle is 25π units squared.
Attention GMAT Students!
To make sure you are not studying endlessly, EduRev has designed GMAT study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in GMAT.
|
Explore Courses for GMAT exam
|
|
Similar GMAT Doubts
Top Courses for GMATView all
On the coordinate plane, each point lying on a circle has its x and y coordinates greater than or equal to zero. If the centre of the circle lies at (3,4), what is the maximum possible area of the circle?a)6πb)8πc)9πd)12πe)16πCorrect answer is option 'C'. Can you explain this answer?
Question Description
On the coordinate plane, each point lying on a circle has its x and y coordinates greater than or equal to zero. If the centre of the circle lies at (3,4), what is the maximum possible area of the circle?a)6πb)8πc)9πd)12πe)16πCorrect answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about On the coordinate plane, each point lying on a circle has its x and y coordinates greater than or equal to zero. If the centre of the circle lies at (3,4), what is the maximum possible area of the circle?a)6πb)8πc)9πd)12πe)16πCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On the coordinate plane, each point lying on a circle has its x and y coordinates greater than or equal to zero. If the centre of the circle lies at (3,4), what is the maximum possible area of the circle?a)6πb)8πc)9πd)12πe)16πCorrect answer is option 'C'. Can you explain this answer?.
On the coordinate plane, each point lying on a circle has its x and y coordinates greater than or equal to zero. If the centre of the circle lies at (3,4), what is the maximum possible area of the circle?a)6πb)8πc)9πd)12πe)16πCorrect answer is option 'C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about On the coordinate plane, each point lying on a circle has its x and y coordinates greater than or equal to zero. If the centre of the circle lies at (3,4), what is the maximum possible area of the circle?a)6πb)8πc)9πd)12πe)16πCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for On the coordinate plane, each point lying on a circle has its x and y coordinates greater than or equal to zero. If the centre of the circle lies at (3,4), what is the maximum possible area of the circle?a)6πb)8πc)9πd)12πe)16πCorrect answer is option 'C'. Can you explain this answer?.
Solutions for On the coordinate plane, each point lying on a circle has its x and y coordinates greater than or equal to zero. If the centre of the circle lies at (3,4), what is the maximum possible area of the circle?a)6πb)8πc)9πd)12πe)16πCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of On the coordinate plane, each point lying on a circle has its x and y coordinates greater than or equal to zero. If the centre of the circle lies at (3,4), what is the maximum possible area of the circle?a)6πb)8πc)9πd)12πe)16πCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
On the coordinate plane, each point lying on a circle has its x and y coordinates greater than or equal to zero. If the centre of the circle lies at (3,4), what is the maximum possible area of the circle?a)6πb)8πc)9πd)12πe)16πCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for On the coordinate plane, each point lying on a circle has its x and y coordinates greater than or equal to zero. If the centre of the circle lies at (3,4), what is the maximum possible area of the circle?a)6πb)8πc)9πd)12πe)16πCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of On the coordinate plane, each point lying on a circle has its x and y coordinates greater than or equal to zero. If the centre of the circle lies at (3,4), what is the maximum possible area of the circle?a)6πb)8πc)9πd)12πe)16πCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice On the coordinate plane, each point lying on a circle has its x and y coordinates greater than or equal to zero. If the centre of the circle lies at (3,4), what is the maximum possible area of the circle?a)6πb)8πc)9πd)12πe)16πCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup