Question

- ( Intercepts form two points form )

If A ( a , b ) and B ( b , a ) lie in 6x-y =1 and 2x - 5y = 5 respectively , find the equation of AB. Show your workings too!

~Thanks in advance! :D ​

Answer 1

Solution given:

A(a,b) lie in 6x-y =1

substituting value of A in equation ,we get

6a-b=1...................(1)

B(b,a) lie in 2x - 5y = 5

substituting value of B in equation ,we get

2b-5a=5

b=5(a+1)/2............(2)

substituting value of b in equation 1 ,we get

6a-5(a+1)/2=1

12a-5a-5=2

7a=2+5

a=
`(7)/(7)`=1

substituting value of a in equation 1 ,we get

6×1-b=1

6-1=b

b=5

so points are A(1,5) and B(5,1)

we have

equation of line having two points

`(y - y1) = (y2 - y1)/(x2 - x1) (x - x1)`

`(y - 5) = (1-5)/(5-1) (x - 1)`

`(y - 5) = -1 (x - 1)`

y-5=1-x

x+y=6 is a required equation of line AB.