Prove that all the lines having the sum of the interceps on the axes equal to half of the product of the intercepts pass through the point. Find the fixed point.

Explanation

Equation of line in intercept from is
`(x)/(a)+(y)/(b) = 1`
` " or " bx+ay=ab " " (1)`
`"Given that " a+b = (ab)/(2)`
`therefore 2a+2b=ab`
So, equation (1) reduces to
bx+ay=2a+2b
`"or " b(x-2)+a(y-2) = 0`
This passes through fixed point (2,2) for all real values of a and b.