JEE Advanced Model Paper 3 with solutions for online practice

Equation of family of circle touching the line x - y = 0 at P(-4, -4) is

(x+4)2 + (y+4)2 + λ (x - y) = 0
x2+y2 + (8 + λ) x + (8 - λ) y + 32 = 0
r = √(

8+λ

2

)2+(

8−λ

2

)2−32
p = |

( −8−λ 2 )−(8+ λ 2 )

√2

| =

16

2√2

=

8

√12

= 4√2
r2 = p2+(3√2)2
⇒ = 32 + 18

2λ

4

= 50
λ2 = 100 ⇒ λ = ± 10

Hence, 2 circles are possible
S1 : x2+y2 + 18x - 2y + 32 = 0
And S2 : x2+y2 - 2x + 18y + 32 = 0
But ( -10 , 2) lies inside S1 = 0
Hence a = -2 , b = 18 , c = 32
∴ (a + b + c) = 48