AP EAPCET 08-Jul-2022 Shift 1 Paper

Given, equation of curve
(

x

a

)x+(

y

b

)x=2
On differentiating w.r.t. x to determine the slope
n(

x

a

)n−1×

1

a

+n(

y

b

)n−1×

1

b

dy

dx

=0
⇒

dy

dx

=−

b

a

(

xb

ya

)n−1=−(

x

y

)n−1(

b

a

)n

dy

dx

|at(a,b)=−(

a

b

)n−1(

b

a

)n=

−b

a

Equation of tangent is
y−b=(−

b

a

)(x−a)
⇒ ay−ab=−bx+ab⇒bx+ay=2ab
⇒

b

2a

+

y

2b

=1
∴ x-intercept is 2a and y - intercept is 2b.
∴ Sum of intercept =2(a+b)