JEE Main 2020 — Circle Question with Solution
From: JEE Main 2020 (Online) 9th January Evening Slot
Question
If the curves, x2 – 6x + y2 + 8 = 0 and
x2 – 8y + y2 + 16 – k = 0, (k > 0) touch each other at a point, then the largest value of k is ______.
x2 – 8y + y2 + 16 – k = 0, (k > 0) touch each other at a point, then the largest value of k is ______.
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Show full solutionCorrect answer: 36
Correct answer
36
Step-by-step explanation
C1 : x2 + y2 – 6x + + 8 = 0
C1(3, 0) and r1 = 1
C2 : x2 + y2 – 8y + 16 – k = 0
C2(0, 4) and r2 =
Two circles touch each other
C1C2 = | r1 r2 |
5 = | 1 |
1 + = 5 or - 1 = 5
k = 16 or k = 36
So largest value of k = 36.
C1(3, 0) and r1 = 1
C2 : x2 + y2 – 8y + 16 – k = 0
C2(0, 4) and r2 =
Two circles touch each other
C1C2 = | r1 r2 |
5 = | 1 |
1 + = 5 or - 1 = 5
k = 16 or k = 36
So largest value of k = 36.
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