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let C1 and C2 be the centres of the circles x2+y2–2x–2y–2 = 0 and x2+y2–6x–6y+14 = 0 respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral PC1QC2 is :
- a)8
- b)6
- c)9
- d)4
Correct answer is option 'D'. Can you explain this answer?
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let C1 and C2 be the centres of the circles x2+y2–2x–2y&nd...
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let C1 and C2 be the centres of the circles x2+y2–2x–2y&nd...
Finding the Centers of the Circles
To find the centers of the circles, we first rewrite the given equations:
- Circle 1: x² + y² - 2x - 2y - 2 = 0
- Completing the square: (x - 1)² + (y - 1)² = 4
- Center C1 = (1, 1)
- Circle 2: x² + y² - 6x - 6y + 14 = 0
- Completing the square: (x - 3)² + (y - 3)² = 4
- Center C2 = (3, 3)
Finding Points of Intersection P and Q
Next, we find the points of intersection P and Q of the two circles:
1. Set the equations equal to each other after rewriting:
- From Circle 1: (x - 1)² + (y - 1)² = 4
- From Circle 2: (x - 3)² + (y - 3)² = 4
2. Solving these gives us the points P and Q, which will be symmetric about the line joining C1 and C2.
Calculating Area of Quadrilateral PC1QC2
The quadrilateral PC1QC2 can be split into two triangles: C1PQC2. The area of this quadrilateral can be calculated using the formula for the area of triangles:
1. Using the coordinates:
- C1 = (1, 1)
- C2 = (3, 3)
- P and Q are symmetric points on the line y = x.
2. The height from C1 to line PQ and the base PQ can be calculated, resulting in an area of 4 square units.
Final Answer
Thus, the area of quadrilateral PC1QC2 is 4 square units, confirming that the correct answer is option 'D'.
To find the centers of the circles, we first rewrite the given equations:
- Circle 1: x² + y² - 2x - 2y - 2 = 0
- Completing the square: (x - 1)² + (y - 1)² = 4
- Center C1 = (1, 1)
- Circle 2: x² + y² - 6x - 6y + 14 = 0
- Completing the square: (x - 3)² + (y - 3)² = 4
- Center C2 = (3, 3)
Finding Points of Intersection P and Q
Next, we find the points of intersection P and Q of the two circles:
1. Set the equations equal to each other after rewriting:
- From Circle 1: (x - 1)² + (y - 1)² = 4
- From Circle 2: (x - 3)² + (y - 3)² = 4
2. Solving these gives us the points P and Q, which will be symmetric about the line joining C1 and C2.
Calculating Area of Quadrilateral PC1QC2
The quadrilateral PC1QC2 can be split into two triangles: C1PQC2. The area of this quadrilateral can be calculated using the formula for the area of triangles:
1. Using the coordinates:
- C1 = (1, 1)
- C2 = (3, 3)
- P and Q are symmetric points on the line y = x.
2. The height from C1 to line PQ and the base PQ can be calculated, resulting in an area of 4 square units.
Final Answer
Thus, the area of quadrilateral PC1QC2 is 4 square units, confirming that the correct answer is option 'D'.
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let C1 and C2 be the centres of the circles x2+y2–2x–2y–2 = 0 and x2+y2–6x–6y+14 = 0 respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral PC1QC2 is :a)8b)6c)9d)4Correct answer is option 'D'. Can you explain this answer?
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let C1 and C2 be the centres of the circles x2+y2–2x–2y–2 = 0 and x2+y2–6x–6y+14 = 0 respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral PC1QC2 is :a)8b)6c)9d)4Correct 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 let C1 and C2 be the centres of the circles x2+y2–2x–2y–2 = 0 and x2+y2–6x–6y+14 = 0 respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral PC1QC2 is :a)8b)6c)9d)4Correct 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 let C1 and C2 be the centres of the circles x2+y2–2x–2y–2 = 0 and x2+y2–6x–6y+14 = 0 respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral PC1QC2 is :a)8b)6c)9d)4Correct answer is option 'D'. Can you explain this answer?.
let C1 and C2 be the centres of the circles x2+y2–2x–2y–2 = 0 and x2+y2–6x–6y+14 = 0 respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral PC1QC2 is :a)8b)6c)9d)4Correct 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 let C1 and C2 be the centres of the circles x2+y2–2x–2y–2 = 0 and x2+y2–6x–6y+14 = 0 respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral PC1QC2 is :a)8b)6c)9d)4Correct 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 let C1 and C2 be the centres of the circles x2+y2–2x–2y–2 = 0 and x2+y2–6x–6y+14 = 0 respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral PC1QC2 is :a)8b)6c)9d)4Correct answer is option 'D'. Can you explain this answer?.
Solutions for let C1 and C2 be the centres of the circles x2+y2–2x–2y–2 = 0 and x2+y2–6x–6y+14 = 0 respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral PC1QC2 is :a)8b)6c)9d)4Correct 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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let C1 and C2 be the centres of the circles x2+y2–2x–2y–2 = 0 and x2+y2–6x–6y+14 = 0 respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral PC1QC2 is :a)8b)6c)9d)4Correct answer is option 'D'. Can you explain this answer?, a detailed solution for let C1 and C2 be the centres of the circles x2+y2–2x–2y–2 = 0 and x2+y2–6x–6y+14 = 0 respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral PC1QC2 is :a)8b)6c)9d)4Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of let C1 and C2 be the centres of the circles x2+y2–2x–2y–2 = 0 and x2+y2–6x–6y+14 = 0 respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral PC1QC2 is :a)8b)6c)9d)4Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice let C1 and C2 be the centres of the circles x2+y2–2x–2y–2 = 0 and x2+y2–6x–6y+14 = 0 respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral PC1QC2 is :a)8b)6c)9d)4Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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