(3)

Given,

The point (p,p + 1) lie inside the region ,

And the set of all values of p is the interval (a, 6),

Now by observation (p,p + 1) lies ony-x = l,

Also point (p,p + 1) lies on x + y = 3

So, solving y - x = 1 and x + y = 3

we get, P(1, 2)

Again given point (p,p + 1) lies on x 2 + y 2 = 9

So, solving y - x = 1 and x 2 + y 2 = 9, we get

x 2 +(l + x) 2 = 9

2x 2 + 2x - 8 = 0

x 2 + x-4 = 0.........(i)

Hence,

Now on comparing with p (a, b) we get,

a = l, b 2 + b = 4 [using (i)]

Hence, the value of 6 2 + 6-a 2 = 4-1 =3

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