JEE Mains Model Paper 8

Let line is

x

a

+

y

b

= 1
∴ A (a, 0) and B (0, b)
Equation of circle since AB is diameters is (x − a) ( x − 0) + ( y − 0) (y − b) = 0
⇒ x2+y2 − ax − by = 0
Tangent at (0, 0) is ax + by = 0
∴ AM = m =

a2

√a2+b2

and BN = n = b

b2

√a2+b2

⇒ m + n = √(a2+b2) = diameter of circle