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If the lines 2x + 3 y + 1 = 0 and 3x -y - 4=0 lie alon g diameter of a circle of circumference 10p, then the equation of the circle is [2004]
- a)x2 + y2 + 2x - 2y - 23=0
- b)x2 + y2 - 2x- 2y - 23=0
- c)x2 + y2 + 2x+ 2y - 23=0
- d)x2 + y2 -2x+ 2y - 23=0
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If the lines 2x + 3 y + 1 = 0 and 3x -y - 4=0 lie alon g diameter of a...
Two diameters are along 2x + 3y +1 = 0 and 3x -y - 4=0
solving we get centre (1, –1) circumference = 2πr = 10π
∴ r= 5.
Required circle is, ( x - 1)2 + (y + 1)2=52
⇒ x2 + y2 -2x+ 2y -23=0
solving we get centre (1, –1) circumference = 2πr = 10π
∴ r= 5.
Required circle is, ( x - 1)2 + (y + 1)2=52
⇒ x2 + y2 -2x+ 2y -23=0
Most Upvoted Answer
If the lines 2x + 3 y + 1 = 0 and 3x -y - 4=0 lie alon g diameter of a...
Given Information:
The equations of the lines are 2x + 3y + 1 = 0 and 3x - y - 4 = 0.
The lines lie along the diameter of a circle with circumference 10π.
Explanation:
- Find the center of the circle:
The center of the circle is the point of intersection of the two lines. Solve the two equations simultaneously to find the center.
- Find the radius of the circle:
The radius of the circle is half the circumference divided by 2π. Calculate the radius using the formula r = Circumference / (2 * π).
- Write the equation of the circle:
The general form of the equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center of the circle and r is the radius. Substitute the values of the center and radius into the equation to get the final equation of the circle.
- Comparing with the given options:
Check which option matches the equation obtained in the previous step.
Therefore, the correct answer is option 'D', which is x^2 + y^2 - 2x + 2y - 23 = 0.
The equations of the lines are 2x + 3y + 1 = 0 and 3x - y - 4 = 0.
The lines lie along the diameter of a circle with circumference 10π.
Explanation:
- Find the center of the circle:
The center of the circle is the point of intersection of the two lines. Solve the two equations simultaneously to find the center.
- Find the radius of the circle:
The radius of the circle is half the circumference divided by 2π. Calculate the radius using the formula r = Circumference / (2 * π).
- Write the equation of the circle:
The general form of the equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center of the circle and r is the radius. Substitute the values of the center and radius into the equation to get the final equation of the circle.
- Comparing with the given options:
Check which option matches the equation obtained in the previous step.
Therefore, the correct answer is option 'D', which is x^2 + y^2 - 2x + 2y - 23 = 0.
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If the lines 2x + 3 y + 1 = 0 and 3x -y - 4=0 lie alon g diameter of a circle of circumference 10p, then the equation of the circle is [2004]a)x2 + y2 + 2x - 2y - 23=0b)x2 + y2 - 2x- 2y - 23=0c)x2 + y2 + 2x+ 2y - 23=0d)x2 + y2 -2x+ 2y - 23=0Correct answer is option 'D'. Can you explain this answer?
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If the lines 2x + 3 y + 1 = 0 and 3x -y - 4=0 lie alon g diameter of a circle of circumference 10p, then the equation of the circle is [2004]a)x2 + y2 + 2x - 2y - 23=0b)x2 + y2 - 2x- 2y - 23=0c)x2 + y2 + 2x+ 2y - 23=0d)x2 + y2 -2x+ 2y - 23=0Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the lines 2x + 3 y + 1 = 0 and 3x -y - 4=0 lie alon g diameter of a circle of circumference 10p, then the equation of the circle is [2004]a)x2 + y2 + 2x - 2y - 23=0b)x2 + y2 - 2x- 2y - 23=0c)x2 + y2 + 2x+ 2y - 23=0d)x2 + y2 -2x+ 2y - 23=0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the lines 2x + 3 y + 1 = 0 and 3x -y - 4=0 lie alon g diameter of a circle of circumference 10p, then the equation of the circle is [2004]a)x2 + y2 + 2x - 2y - 23=0b)x2 + y2 - 2x- 2y - 23=0c)x2 + y2 + 2x+ 2y - 23=0d)x2 + y2 -2x+ 2y - 23=0Correct answer is option 'D'. Can you explain this answer?.
If the lines 2x + 3 y + 1 = 0 and 3x -y - 4=0 lie alon g diameter of a circle of circumference 10p, then the equation of the circle is [2004]a)x2 + y2 + 2x - 2y - 23=0b)x2 + y2 - 2x- 2y - 23=0c)x2 + y2 + 2x+ 2y - 23=0d)x2 + y2 -2x+ 2y - 23=0Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If the lines 2x + 3 y + 1 = 0 and 3x -y - 4=0 lie alon g diameter of a circle of circumference 10p, then the equation of the circle is [2004]a)x2 + y2 + 2x - 2y - 23=0b)x2 + y2 - 2x- 2y - 23=0c)x2 + y2 + 2x+ 2y - 23=0d)x2 + y2 -2x+ 2y - 23=0Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the lines 2x + 3 y + 1 = 0 and 3x -y - 4=0 lie alon g diameter of a circle of circumference 10p, then the equation of the circle is [2004]a)x2 + y2 + 2x - 2y - 23=0b)x2 + y2 - 2x- 2y - 23=0c)x2 + y2 + 2x+ 2y - 23=0d)x2 + y2 -2x+ 2y - 23=0Correct answer is option 'D'. Can you explain this answer?.
Solutions for If the lines 2x + 3 y + 1 = 0 and 3x -y - 4=0 lie alon g diameter of a circle of circumference 10p, then the equation of the circle is [2004]a)x2 + y2 + 2x - 2y - 23=0b)x2 + y2 - 2x- 2y - 23=0c)x2 + y2 + 2x+ 2y - 23=0d)x2 + y2 -2x+ 2y - 23=0Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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