JEE Main 2021 — Circle Question with Solution
From: JEE Main 2021 (Online) 31st August Morning Shift
Question
If the variable line 3x + 4y = lies between the two
circles (x 1)2 + (y 1)2 = 1
and (x 9)2 + (y 1)2 = 4, without intercepting a chord on either circle, then the sum of all the integral values of is ___________.
circles (x 1)2 + (y 1)2 = 1
and (x 9)2 + (y 1)2 = 4, without intercepting a chord on either circle, then the sum of all the integral values of is ___________.
Enter your answer
Show full solutionCorrect answer: 165
Correct answer
165
Step-by-step explanation
Both centers should lie on either side of the line as well as line can be tangent to circle.
(3 + 4 ) . (27 + 4 ) < 0
(7 ) . (31 ) < 0 (7, 31) ....... (1)
d1 = distance of (1, 1) from line
d2 = distance of (9, 1) from line
.... (2)
....(3)
(1) (2) (3) [12, 21]
Sum of integers = 165
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