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JEE Main 202117 MarchMorning Shift
Exam
JEE Main
Year
2021
Date
17 March
Shift
Morning Shift
Subject
Mathematics
Chapter
Circle

JEE Main 2021 · 17 March · Morning Shift · Mathematics · Circle

The minimum distance between any two points P _ 1 and P _ 2 while...

The minimum distance between any two points P1{P}_{1} and P2{P}_{2} while considering point P1{P}_{1} on one circle and point P2{P}_{2} on the other circle for the given circles' equations

x2+y2−10x−10y+41=0{x}^{2} + {y}^{2} - 10x - 10y + 41 = 0

x2+y2−24x−10y+160=0{x}^{2} + {y}^{2} - 24x - 10y + 160 = 0 is ________

The minimum distance between any two points P _ 1 and P _ 2 while considering point P _ 1 on one circle and point P _ 2

Correct answer

0

Step-by-step solution

Given C1(5,5),r1=3{C}_{1} ( 5, 5 ) , {r}_{1} = 3 and C2(12,5),r2=3{C}_{2} ( 12, 5 ) , {r}_{2} = 3

C1C2=7{C}_{1}{C}_{2} = 7

Now, C1C2>r1+r2{C}_{1}{C}_{2} > {r}_{1} + {r}_{2}

Thus, {\left({P}_{1}{P}_{2}\right)}_\min = 7 - 6 = 1

The minimum distance between any two points P _ 1 and P _ 2 while considering point P _ 1 on one circle and point P _ 2

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