JEE Main 2017 — Circle Question with Solution
From: JEE Main 2017 (Offline)
Question
The radius of a circle, having minimum area, which touches the curve y = 4 – x2 and the lines, y = |x| is :
Choose an option
Show full solutionCorrect option: B
Correct answer
B
Step-by-step explanation
Let the radius of circle with least area be r.
Then, the coordinate of the center = (0, b)
The equation of circle be x2 + (y – b)2 = r2
Distance of perpendiculur from (0, 4) to y = x line = r
b =
Circle passes through (0, 4),
0 + (4 – b)2 = r2
4 - b = r
4 - = r
r = =
Then, the coordinate of the center = (0, b)
The equation of circle be x2 + (y – b)2 = r2
Distance of perpendiculur from (0, 4) to y = x line = r
b =
Circle passes through (0, 4),
0 + (4 – b)2 = r2
4 - b = r
4 - = r
r = =
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This is a previous-year question from JEE Main 2017, covering the Circle chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.