JEE Exam  >  JEE Questions  >  A circle is given by x2 + (y–1)2 = 1, a... Start Learning for Free
A circle is given by x2 + (y–1)2 = 1, another circle C touches it externally and also the x-axis, then the locus of its centre is (2005S)
  • a)
    {(x, y) : x2 = 4y} ∪ {(x, y) : y ≤ 0}
  • b)
    {(x, y) : x2 + (y – 1)2 = 4}∪  {(x, y) : y ≤ 0}
  • c)
    {(x, y) : x2 = y} ∪ {(0, y) : y ≤ 0}
  • d)
    {(x, y) : x2 = 4y} ∪ {(0, y) : y ≤ 0}
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A circle is given by x2 + (y–1)2 = 1, another circle C touches i...
Let the centre of circle C be (h, k). Then as this circle touches axis of x, its radius = | k |
Also it touches the given circle x2 + (y – 1)2 = 1, centre (0, 1) radius 1, externally
Therefore, the distance between centres = sum of radii
⇒ h2 + k2 – 2k + 1 = (1 + | k |)2
⇒ h2 +  k2 – 2k + 1 = 1 + 2 | k | + k2
⇒ h2 = 2k + 2 | k |
∴ Locus of (h, k) is, x2 = 2y + 2 | y |
Now if y > 0, it becomes x2 = 4y and if y < 0, it becomes x = 0
∴ Combining the two, the required locus is {(x, y) : x2 = 4y} ∪ {(0, y) : y < 0}
View all questions of this test
Most Upvoted Answer
A circle is given by x2 + (y–1)2 = 1, another circle C touches i...
A circle is given by the equation x^2 + y^2 = r^2, where r is the radius of the circle.
Explore Courses for JEE exam
Question Description
A circle is given by x2 + (y–1)2 = 1, another circle C touches it externally and also the x-axis, then the locus of its centre is (2005S)a){(x, y) : x2 = 4y} ∪ {(x, y) : y ≤ 0}b){(x, y) : x2 + (y – 1)2 = 4}∪ {(x, y) : y ≤ 0}c){(x, y) : x2 = y} ∪ {(0, y) : y ≤ 0}d){(x, y) : x2 = 4y} ∪ {(0, y) : y ≤ 0}Correct answer is option 'D'. 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 A circle is given by x2 + (y–1)2 = 1, another circle C touches it externally and also the x-axis, then the locus of its centre is (2005S)a){(x, y) : x2 = 4y} ∪ {(x, y) : y ≤ 0}b){(x, y) : x2 + (y – 1)2 = 4}∪ {(x, y) : y ≤ 0}c){(x, y) : x2 = y} ∪ {(0, y) : y ≤ 0}d){(x, y) : x2 = 4y} ∪ {(0, y) : y ≤ 0}Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circle is given by x2 + (y–1)2 = 1, another circle C touches it externally and also the x-axis, then the locus of its centre is (2005S)a){(x, y) : x2 = 4y} ∪ {(x, y) : y ≤ 0}b){(x, y) : x2 + (y – 1)2 = 4}∪ {(x, y) : y ≤ 0}c){(x, y) : x2 = y} ∪ {(0, y) : y ≤ 0}d){(x, y) : x2 = 4y} ∪ {(0, y) : y ≤ 0}Correct answer is option 'D'. Can you explain this answer?.
Solutions for A circle is given by x2 + (y–1)2 = 1, another circle C touches it externally and also the x-axis, then the locus of its centre is (2005S)a){(x, y) : x2 = 4y} ∪ {(x, y) : y ≤ 0}b){(x, y) : x2 + (y – 1)2 = 4}∪ {(x, y) : y ≤ 0}c){(x, y) : x2 = y} ∪ {(0, y) : y ≤ 0}d){(x, y) : x2 = 4y} ∪ {(0, y) : y ≤ 0}Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of A circle is given by x2 + (y–1)2 = 1, another circle C touches it externally and also the x-axis, then the locus of its centre is (2005S)a){(x, y) : x2 = 4y} ∪ {(x, y) : y ≤ 0}b){(x, y) : x2 + (y – 1)2 = 4}∪ {(x, y) : y ≤ 0}c){(x, y) : x2 = y} ∪ {(0, y) : y ≤ 0}d){(x, y) : x2 = 4y} ∪ {(0, y) : y ≤ 0}Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of A circle is given by x2 + (y–1)2 = 1, another circle C touches it externally and also the x-axis, then the locus of its centre is (2005S)a){(x, y) : x2 = 4y} ∪ {(x, y) : y ≤ 0}b){(x, y) : x2 + (y – 1)2 = 4}∪ {(x, y) : y ≤ 0}c){(x, y) : x2 = y} ∪ {(0, y) : y ≤ 0}d){(x, y) : x2 = 4y} ∪ {(0, y) : y ≤ 0}Correct answer is option 'D'. Can you explain this answer?, a detailed solution for A circle is given by x2 + (y–1)2 = 1, another circle C touches it externally and also the x-axis, then the locus of its centre is (2005S)a){(x, y) : x2 = 4y} ∪ {(x, y) : y ≤ 0}b){(x, y) : x2 + (y – 1)2 = 4}∪ {(x, y) : y ≤ 0}c){(x, y) : x2 = y} ∪ {(0, y) : y ≤ 0}d){(x, y) : x2 = 4y} ∪ {(0, y) : y ≤ 0}Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of A circle is given by x2 + (y–1)2 = 1, another circle C touches it externally and also the x-axis, then the locus of its centre is (2005S)a){(x, y) : x2 = 4y} ∪ {(x, y) : y ≤ 0}b){(x, y) : x2 + (y – 1)2 = 4}∪ {(x, y) : y ≤ 0}c){(x, y) : x2 = y} ∪ {(0, y) : y ≤ 0}d){(x, y) : x2 = 4y} ∪ {(0, y) : y ≤ 0}Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice A circle is given by x2 + (y–1)2 = 1, another circle C touches it externally and also the x-axis, then the locus of its centre is (2005S)a){(x, y) : x2 = 4y} ∪ {(x, y) : y ≤ 0}b){(x, y) : x2 + (y – 1)2 = 4}∪ {(x, y) : y ≤ 0}c){(x, y) : x2 = y} ∪ {(0, y) : y ≤ 0}d){(x, y) : x2 = 4y} ∪ {(0, y) : y ≤ 0}Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
Explore Courses for JEE exam

Top Courses for JEE

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev