Let R be the region of the disc x^2+y^2\leq1 in the first quadrant. Then the area of the largest possible circle contained in R is

KVPY SX SB Exam 05-Nov-2017 Question Paper

Question : 86 of 120

Marks: +1, -0

Let R be the region of the disc

x^2+y^2≤1

in the first quadrant. Then the area of the largest possible circle contained in R is

Solution:

Required equation of circle

(x -h)^2 + (y - h)^2 = h^2

Both circle touch internally

C_1C_2 = |r_1 - r_2|

√{h ^2+ h^2} ={ |h - 1|}

Solve this

h = √2 -1

Area

π( √2 -1)^2 = π(3 -2 √2 )

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