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The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then, the equation of the circle is
- a)x2 + y2 + 2x - 2y = 47
- b)x2 + y2 - 2x + 2y = 47
- c)x2 + y2 - 2x + 2y = 62
- d)x2 + y2 + 2x - 2y = 62
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle havin...
To find the equation of the circle, we need to find the coordinates of the center and the radius of the circle.
Finding the center of the circle:
1. Rewrite the given equations in the standard form of a circle: (x - h)^2 + (y - k)^2 = r^2.
2. Let's start with the first equation, 2x - 3y = 5.
- Rewrite it as: 2x - 5 = 3y.
- Divide both sides by 3: (2/3)x - (5/3) = y.
- Now we have y = (2/3)x - (5/3), which can be written as y = (2/3)(x - 0) - (5/3).
- Comparing this with the standard form, we see that h = 0 and k = -5/3.
3. Similarly, for the second equation, 3x - 4y = 7.
- Rewrite it as: 3x - 7 = 4y.
- Divide both sides by 4: (3/4)x - (7/4) = y.
- Now we have y = (3/4)x - (7/4), which can be written as y = (3/4)(x - 0) - (7/4).
- Comparing this with the standard form, we see that h = 0 and k = -7/4.
From the above calculations, we can conclude that the center of the circle is (0, -5/3) or (0, -7/4).
Finding the radius of the circle:
1. Rewrite the given equations in slope-intercept form: y = mx + c.
2. Let's start with the first equation, 2x - 3y = 5.
- Rewrite it as: y = (2/3)x - 5/3.
- Comparing this with the slope-intercept form, we see that the slope m = 2/3.
3. Similarly, for the second equation, 3x - 4y = 7.
- Rewrite it as: y = (3/4)x - 7/4.
- Comparing this with the slope-intercept form, we see that the slope m = 3/4.
From the above calculations, we can conclude that the slopes of the diameters are 2/3 and 3/4.
The radius of a circle is perpendicular to the diameter. Therefore, the product of the slopes of the diameters will be -1.
(2/3) * (3/4) = 6/12 = 1/2 ≠ -1.
Since the product of the slopes is not -1, the given lines do not form diameters of a circle. Hence, the given information is incorrect.
Therefore, none of the options provided (A, B, C, D) is the correct equation of the circle.
Finding the center of the circle:
1. Rewrite the given equations in the standard form of a circle: (x - h)^2 + (y - k)^2 = r^2.
2. Let's start with the first equation, 2x - 3y = 5.
- Rewrite it as: 2x - 5 = 3y.
- Divide both sides by 3: (2/3)x - (5/3) = y.
- Now we have y = (2/3)x - (5/3), which can be written as y = (2/3)(x - 0) - (5/3).
- Comparing this with the standard form, we see that h = 0 and k = -5/3.
3. Similarly, for the second equation, 3x - 4y = 7.
- Rewrite it as: 3x - 7 = 4y.
- Divide both sides by 4: (3/4)x - (7/4) = y.
- Now we have y = (3/4)x - (7/4), which can be written as y = (3/4)(x - 0) - (7/4).
- Comparing this with the standard form, we see that h = 0 and k = -7/4.
From the above calculations, we can conclude that the center of the circle is (0, -5/3) or (0, -7/4).
Finding the radius of the circle:
1. Rewrite the given equations in slope-intercept form: y = mx + c.
2. Let's start with the first equation, 2x - 3y = 5.
- Rewrite it as: y = (2/3)x - 5/3.
- Comparing this with the slope-intercept form, we see that the slope m = 2/3.
3. Similarly, for the second equation, 3x - 4y = 7.
- Rewrite it as: y = (3/4)x - 7/4.
- Comparing this with the slope-intercept form, we see that the slope m = 3/4.
From the above calculations, we can conclude that the slopes of the diameters are 2/3 and 3/4.
The radius of a circle is perpendicular to the diameter. Therefore, the product of the slopes of the diameters will be -1.
(2/3) * (3/4) = 6/12 = 1/2 ≠ -1.
Since the product of the slopes is not -1, the given lines do not form diameters of a circle. Hence, the given information is incorrect.
Therefore, none of the options provided (A, B, C, D) is the correct equation of the circle.
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Community Answer
The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle havin...
Coordinate of centre is equal to intersection point of diameters, which is (1, -1).
πR2 = 154, R2 = 49
∴ R = 7
∴ Required equation of circle,
(x - 1)2 + (y + 1)2 = 49
x2 + y2 - 2x + 2y = 47
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The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then, the equation of the circle isa)x2 + y2 + 2x - 2y = 47b)x2 + y2 - 2x + 2y = 47c)x2 + y2 - 2x + 2y = 62d)x2 + y2 + 2x - 2y = 62Correct answer is option 'B'. Can you explain this answer?
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The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then, the equation of the circle isa)x2 + y2 + 2x - 2y = 47b)x2 + y2 - 2x + 2y = 47c)x2 + y2 - 2x + 2y = 62d)x2 + y2 + 2x - 2y = 62Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then, the equation of the circle isa)x2 + y2 + 2x - 2y = 47b)x2 + y2 - 2x + 2y = 47c)x2 + y2 - 2x + 2y = 62d)x2 + y2 + 2x - 2y = 62Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then, the equation of the circle isa)x2 + y2 + 2x - 2y = 47b)x2 + y2 - 2x + 2y = 47c)x2 + y2 - 2x + 2y = 62d)x2 + y2 + 2x - 2y = 62Correct answer is option 'B'. Can you explain this answer?.
The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then, the equation of the circle isa)x2 + y2 + 2x - 2y = 47b)x2 + y2 - 2x + 2y = 47c)x2 + y2 - 2x + 2y = 62d)x2 + y2 + 2x - 2y = 62Correct answer is option 'B'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then, the equation of the circle isa)x2 + y2 + 2x - 2y = 47b)x2 + y2 - 2x + 2y = 47c)x2 + y2 - 2x + 2y = 62d)x2 + y2 + 2x - 2y = 62Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then, the equation of the circle isa)x2 + y2 + 2x - 2y = 47b)x2 + y2 - 2x + 2y = 47c)x2 + y2 - 2x + 2y = 62d)x2 + y2 + 2x - 2y = 62Correct answer is option 'B'. Can you explain this answer?.
Solutions for The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then, the equation of the circle isa)x2 + y2 + 2x - 2y = 47b)x2 + y2 - 2x + 2y = 47c)x2 + y2 - 2x + 2y = 62d)x2 + y2 + 2x - 2y = 62Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then, the equation of the circle isa)x2 + y2 + 2x - 2y = 47b)x2 + y2 - 2x + 2y = 47c)x2 + y2 - 2x + 2y = 62d)x2 + y2 + 2x - 2y = 62Correct answer is option 'B'. Can you explain this answer?, a detailed solution for The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then, the equation of the circle isa)x2 + y2 + 2x - 2y = 47b)x2 + y2 - 2x + 2y = 47c)x2 + y2 - 2x + 2y = 62d)x2 + y2 + 2x - 2y = 62Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then, the equation of the circle isa)x2 + y2 + 2x - 2y = 47b)x2 + y2 - 2x + 2y = 47c)x2 + y2 - 2x + 2y = 62d)x2 + y2 + 2x - 2y = 62Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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