JEE Main 2021 — Circle Question with Solution
From: JEE Main 2021 (Online) 22th July Evening Shift
Question
Let the circle S : 36x2 + 36y2 108x + 120y + C = 0 be such that it neither intersects nor touches the co-ordinate axes. If the point of intersection of the lines, x 2y = 4 and 2x y = 5 lies inside the circle S, then :
Choose an option
Show full solutionCorrect option: D
Correct answer
D100 < C < 156
Step-by-step explanation
S : 36x2 + 36y2 108x + 120y + C = 0
x2 + y2 3x + y + = 0
Centre
radius =
Now,
C > 100 ...... (1)
Now, point of intersection of x 2y = 4 and 2x y = 5 is (2, 1), which lies inside the circle S.
S(2, 1) < 0
(2)2 + (1)2 3(2) + (1) + < 0
4 + 1 6 + < 0
C < 156 ..... (2)
From (1) & (2)
100 < C < 156 Ans.
x2 + y2 3x + y + = 0
Centre
radius =
Now,
C > 100 ...... (1)
Now, point of intersection of x 2y = 4 and 2x y = 5 is (2, 1), which lies inside the circle S.
S(2, 1) < 0
(2)2 + (1)2 3(2) + (1) + < 0
4 + 1 6 + < 0
C < 156 ..... (2)
From (1) & (2)
100 < C < 156 Ans.
Practice this on the real CBT interface
Solve this JEE Main question (and the rest of the Circle chapter) on PrepSharp's TCS iON-style CBT player — with timer, bookmarks and session analytics.
Solve interactively →About this question
This is a previous-year question from JEE Main 2021, 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.