UPSC NDA Math Model Paper 3

Intercept form of the line is

x

a

+

y

b

=1 At x axis point is A (a, 0)
At y axis point is B (0, b)
Case 1: Given point P (2, 3) divides A and B in ratio of m : n = 3 : 2
Applying Internal Section Formula,
We know that (x,y)=(

mx2+nx1

m+n

,

my2+my1

m+n

)
⇒(2,3)=(

3(0)+2(a)

3+2

,

3(b)+2(0)

3+2

)
⇒(2,3)=(

2a

5

,

3b

5

)
Now,

2a

5

=2 and

3b

5

=3
⇒a=5 and b=5
∴ Equation of line is

x

5

+

y

5

=1⇒x+y=5
Case 2: Given point P (2, 3) divides A and B in ratio of m : n = 2 : 3
⇒(2,3)=(

2(0)+3(a)

3+2

,

2(b)+3(0)

3+2

)
⇒(2,3)=(

3a

5

,

2b

5

)
Now,

3a

5

=2 and

2b

5

=3
⇒ a = 10/3 and b = 15/2
∴ Equation of line is

x

(10∕3)

+

y

(15∕2)

=1
⇒

3x

10

+

2

15

=1
⇒9x+4y=30