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The equation of the smallest circle passing through the intersection of the line x + y = 1 and the circle x2 + y2 = 9 is
- a)x2 + y2 + x + y − 8 = 0
- b)x2 + y2 − x − y − 8 = 0
- c)x2 + y2 − x + y − 8 = 0
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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The equation of the smallest circle passing through the intersection o...
Given Equations:
- Line: x + y = 1
- Circle: x^2 + y^2 = 9
Finding the Intersection Point:
1. Substitute y = 1 - x into the equation of the circle:
x^2 + (1 - x)^2 = 9
2x^2 - 2x - 8 = 0
x^2 - x - 4 = 0
(x - 2)(x + 2) = 0
x = 2 or x = -2
Intersection Points:
When x = 2, y = 1 - 2 = -1
When x = -2, y = 1 - (-2) = 3
So, the intersection points are (2, -1) and (-2, 3)
Equation of the Circle Passing Through the Intersection Points:
1. The general equation of a circle is (x - h)^2 + (y - k)^2 = r^2.
2. Substitute the intersection points into the general equation:
At (2, -1): (2 - h)^2 + (-1 - k)^2 = r^2
At (-2, 3): (-2 - h)^2 + (3 - k)^2 = r^2
3. Solving the above two equations will give us the values of h, k, and r.
Correct Answer:
The correct equation of the smallest circle passing through the intersection of the given line and circle is x^2 + y^2 - x - y - 8 = 0, which corresponds to option B.
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The equation of the smallest circle passing through the intersection o...
Just check radius value u got answer
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The equation of the smallest circle passing through the intersection of the line x + y = 1 and the circle x2+ y2= 9 isa)x2+ y2+ x + y − 8 = 0b)x2+ y2− x − y − 8 = 0c)x2+ y2− x + y − 8 = 0d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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The equation of the smallest circle passing through the intersection of the line x + y = 1 and the circle x2+ y2= 9 isa)x2+ y2+ x + y − 8 = 0b)x2+ y2− x − y − 8 = 0c)x2+ y2− x + y − 8 = 0d)None of theseCorrect answer is option 'B'. 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 The equation of the smallest circle passing through the intersection of the line x + y = 1 and the circle x2+ y2= 9 isa)x2+ y2+ x + y − 8 = 0b)x2+ y2− x − y − 8 = 0c)x2+ y2− x + y − 8 = 0d)None of theseCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The equation of the smallest circle passing through the intersection of the line x + y = 1 and the circle x2+ y2= 9 isa)x2+ y2+ x + y − 8 = 0b)x2+ y2− x − y − 8 = 0c)x2+ y2− x + y − 8 = 0d)None of theseCorrect answer is option 'B'. Can you explain this answer?.
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