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A circle touches both the y-axis and the line x + y = 0. Then the locus of its centre is
- a)y = √2x
- b)x = √2y
- c)y2 - x2 = 2xy
- d)x2 - y2 = 2xy
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A circle touches both the y-axis and the line x + y = 0. Then the locu...
The locus of the center of the circle is the line x = -r, where r is the radius of the circle.
To see why, draw a diagram:
- The circle touches the y-axis at a point (0, r) or (0, -r), depending on whether it is above or below the x-axis.
- The circle also touches the line x + y = 0 at a point (-r, r) or (r, -r), depending on whether it is to the left or right of the y-axis.
- The center of the circle must be equidistant from these two points, so it lies on the line that passes through them.
That line is x + y = 0 (since (-r, r) and (r, -r) both satisfy this equation), but we want to express it in terms of x only. Solving for y, we get y = -x. Thus, the locus of the center of the circle is x = -r, which is a vertical line to the left (or right, if r is negative) of the y-axis.
To see why, draw a diagram:
- The circle touches the y-axis at a point (0, r) or (0, -r), depending on whether it is above or below the x-axis.
- The circle also touches the line x + y = 0 at a point (-r, r) or (r, -r), depending on whether it is to the left or right of the y-axis.
- The center of the circle must be equidistant from these two points, so it lies on the line that passes through them.
That line is x + y = 0 (since (-r, r) and (r, -r) both satisfy this equation), but we want to express it in terms of x only. Solving for y, we get y = -x. Thus, the locus of the center of the circle is x = -r, which is a vertical line to the left (or right, if r is negative) of the y-axis.
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A circle touches both the y-axis and the line x + y = 0. Then the locu...
Let the centre be (h, k).
⇒ 2h2 = h2 + k2 + 2hk
The locus will be x2 - y2 = 2xy.
⇒ 2h2 = h2 + k2 + 2hk
The locus will be x2 - y2 = 2xy.
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A circle touches both the y-axis and the line x + y = 0. Then the locus of its centre isa)y =√2xb)x =√2yc)y2 - x2 = 2xyd)x2 - y2 = 2xyCorrect answer is option 'D'. Can you explain this answer?
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A circle touches both the y-axis and the line x + y = 0. Then the locus of its centre isa)y =√2xb)x =√2yc)y2 - x2 = 2xyd)x2 - y2 = 2xyCorrect 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 A circle touches both the y-axis and the line x + y = 0. Then the locus of its centre isa)y =√2xb)x =√2yc)y2 - x2 = 2xyd)x2 - y2 = 2xyCorrect 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 A circle touches both the y-axis and the line x + y = 0. Then the locus of its centre isa)y =√2xb)x =√2yc)y2 - x2 = 2xyd)x2 - y2 = 2xyCorrect answer is option 'D'. Can you explain this answer?.
A circle touches both the y-axis and the line x + y = 0. Then the locus of its centre isa)y =√2xb)x =√2yc)y2 - x2 = 2xyd)x2 - y2 = 2xyCorrect 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 A circle touches both the y-axis and the line x + y = 0. Then the locus of its centre isa)y =√2xb)x =√2yc)y2 - x2 = 2xyd)x2 - y2 = 2xyCorrect 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 A circle touches both the y-axis and the line x + y = 0. Then the locus of its centre isa)y =√2xb)x =√2yc)y2 - x2 = 2xyd)x2 - y2 = 2xyCorrect answer is option 'D'. Can you explain this answer?.
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