Question

A line AB cut off intercepts on the axes in such a way that the sum and the product of the intercepts are 1 and -6 respectively, then find the value of a and b.

Please help
please please please please please please please please please please please please please please please please please please please please please please please please​

Answer 1

Answer:

Equation of a line by intercept form is

a

x

+

b

y

=1

where

a=x-intercept

b=y-intercept

But given that x and y intercept are equal in magnitude but opposite in sign

∴a=−b or b=−a

Thus, equation of line is

a

x

−

a

y

=1

x−y=a

x−y−a=0......(1)

Since the line is passing through (2,3)

∴ Point (2,3) will satisfy equation of line

Putting x=2 and y=3 in (1)

2−3−a=0

−1−a=0

a=−1

Now, equation of line become

x−y+1=0

This is the required equation.