Circle

Let the ends of diameter of the given circle x2+y2=4 is (2‌cos‌θ,2sin‌θ), then other must be (−2‌cos‌θ,−2sin‌θ)
Then, length of perpendicular from the extremities of diameter to the line x+y+1=0 is
‌‌

2(cos‌θ+sin‌θ)+1

√2

‌×‌

−2(cos‌θ+sin‌θ)+1

√2

=P(‌ say ‌)
‌⇒P=‌

1−4(cos‌θ+sin‌θ)2

2

‌=‌

1−4(1+sin‌2θ)

2

‌⇒P=‌

−3−4sin‌2θ

2

‌⇒‌‌‌

dP

dθ

=‌

1

2

(−4)‌cos‌2‌θ⋅2=0
‌⇒‌‌cos‌2‌θ=0⇒2θ=‌

π

2

‌θ=‌

π

4

Hence, the points are (√2,√2) and (−√2,−√2)