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For a point P in the plane, let d1 (P) a...

For a point P in the plane, let d1 (P) and d2 (P) be the distance of the point P from the lines x – y = 0 and x + y = 0 respectively. The area of the region R consisting of all points P lying in the first quadrant of the plane and satisfying 2 < d1(P) + d2 (P)< 4, is

Text Solution

Verified by Experts

let the point be `(h,k)`
for a given line, `ax+by+c`
`d= |(ah+bk+c)/sqrt(a^2+b^2)|`
so, `2 <= d_1p + d_2p <= 4`
`2 <= |(h-k)/sqrt 2| + |(h+k)/sqrt 2| <= 4`
`2sqrt2 <= |h-k| + |h+k|`
`if h>k `
`2sqrt2 <= h-k+h+k <= 4sqrt2 `
...
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