Question

let p(x,y) be any point on the line joining the points A(a,0) and B(b,0) show that x by a + y by b=1

Answer 1

Equation of the line isAx+By+C=0 equation 1
If x-interception is A(a,0)M(a,0) and y-interception is B(0,b)N(0,b) then they need to satisfy line equation
then 
Aa+C=0 equation 2
Bb+C=0  equtaion 3


now 
A=−C/a;  equation a 

B=−C/b; equation b 

substitute the a and b in equation 1

and take C common 
 and you will get the equation i.e 

x/a + y/b =1