UPSC NDA Math Model Paper 3

Given: The straight line

x

a

+

y

b

=1 passes through the points (8, - 9) and (12, - 15)
i.e The points (8, - 9) and (12, - 15) will satisfy the equation

x

a

+

y

b

=1
⇒

8

a

−

9

b

=1− .........(1)
⇒

12

a

−

15

b

=1 ........(2)
From equation (1) and (2), we get
⇒

8

a

−

9

b

=

12

a

−

15

b

⇒ a = 2b/3 .......(2)
By substituting a = 2b/3 in the equation (1), we get
⇒

24

2b

−

9

b

=1
⇒ b = 3
So by substituting b = 3 in (2), we get
⇒ a = 2
Hence, option C is the correct answer