JEE Advanced 2020 Concept Recapitulation Test 3 Paper 1

Equation of bisectors are given by x−y=0 and x+y+z=0
Bisector intersect at the point P(−1,−1)
Focus S, is the foot of parallel from P to MN
Where M(1,1) and N(0,−2)
MN⇒3x−y−z=0,‌‌PS=x+3y+4=0
∴ Focus =(‌

1

5

,‌

−7

5

),MS=√‌

2

5

,NS=4√‌

2

5

LR=‌

16√2

53∕2

Circle through PMN is x2+y2−x+y−2=0
Equation of directrix = equation of tangents at (−1,−1) is 3x+y+4=0