AP EAPCET 25-Aug-2021 Shift 2 Paper

Since, intercept form of line is

x

a

+

y

b

=1
where X-intercept =a,Y-intercept =b Hence, equation of line AB

x

m

+

y

n

=1 ...(i)
∵ Line (i) passes through (4,5).
∴

4

n

+

5

n

=1

4

m

=1−

5

n

m=

4n

n−5

∵ Area of Δ‌OAB=

1

2

×OA×OB
A=

1

2

mn=

1

2

(

4n

n−5

)n
A=

2n2

n−5

∴

dA

dn

=2{

(n−5).2n−n2(1)

(n−5)2

}

dA

dn

=2{

2n2−10n−n2

(n−5)2

}
=

2n2−20n

(n−5)2

∵ Area is least for some value of n.
∴

dA

dn

=0
2n2−20n=0
2n(n−10)=0
⇒ n=0,10
At n=10,m=

4n

n−5

=

4×10

10−5

=

40

5

m = 8
∴ m:n=8:10=4:5