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If the circle x2 + y2 = 9 touches the circle x2 + y2 + 6y + c = 0, then c is equal to
- a)27
- b)36
- c)–36
- d)–27
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If the circle x2+ y2= 9 touches the circle x2+ y2+ 6y + c = 0, then c ...
touches the another circle
Now, Central first circle will be
And its radius will be 3 units.
Also,centre of second circle
And radius,
As both touches each other
So,
Most Upvoted Answer
If the circle x2+ y2= 9 touches the circle x2+ y2+ 6y + c = 0, then c ...
To determine the value of c, we need to find the equation of the circle that touches the circle x^2 + y^2 = 9 and x^2 + y^2 - 6y + c = 0.
To find the equation of the circle that touches both circles, we need to find the common tangent of the two circles.
The first circle x^2 + y^2 = 9 has center (0,0) and radius 3.
The second circle x^2 + y^2 - 6y + c = 0 has center (0,3) and radius sqrt(c).
The distance between the centers of the two circles is the difference in their y-coordinates, which is 3.
Since the two circles touch each other, the distance between their centers should be equal to the sum of their radii.
Therefore, 3 + sqrt(c) = 3.
Simplifying the equation, we get sqrt(c) = 0.
Squaring both sides of the equation, we get c = 0.
Therefore, c is equal to 0.
Answer: c) 0
To find the equation of the circle that touches both circles, we need to find the common tangent of the two circles.
The first circle x^2 + y^2 = 9 has center (0,0) and radius 3.
The second circle x^2 + y^2 - 6y + c = 0 has center (0,3) and radius sqrt(c).
The distance between the centers of the two circles is the difference in their y-coordinates, which is 3.
Since the two circles touch each other, the distance between their centers should be equal to the sum of their radii.
Therefore, 3 + sqrt(c) = 3.
Simplifying the equation, we get sqrt(c) = 0.
Squaring both sides of the equation, we get c = 0.
Therefore, c is equal to 0.
Answer: c) 0
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If the circle x2+ y2= 9 touches the circle x2+ y2+ 6y + c = 0, then c is equal toa)27b)36c)–36d)–27Correct answer is option 'A'. 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 If the circle x2+ y2= 9 touches the circle x2+ y2+ 6y + c = 0, then c is equal toa)27b)36c)–36d)–27Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the circle x2+ y2= 9 touches the circle x2+ y2+ 6y + c = 0, then c is equal toa)27b)36c)–36d)–27Correct answer is option 'A'. Can you explain this answer?.
If the circle x2+ y2= 9 touches the circle x2+ y2+ 6y + c = 0, then c is equal toa)27b)36c)–36d)–27Correct answer is option 'A'. 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 If the circle x2+ y2= 9 touches the circle x2+ y2+ 6y + c = 0, then c is equal toa)27b)36c)–36d)–27Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the circle x2+ y2= 9 touches the circle x2+ y2+ 6y + c = 0, then c is equal toa)27b)36c)–36d)–27Correct answer is option 'A'. Can you explain this answer?.
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