Question

a variable line passes through fixed point (a,b) and meets the coordinate axes in a and b. the locus of the point of intersection of lines through a,b and parallel to coordinate axes is

Answer 1

The  locus of the point of intersection of lines through a,b and parallel to coordinate axes is 1.

Step-by-step explanation:

Let slope of line be m then equation of line

y − b = m(x−a)

At point A

y=0

−b=m(x−a)

or x=(  m −b  )+a

At point B

x=0

y − b = m(0−a)

y = − ma+b

h = (  m −b  )+a  --------(1)

and K = −ma + b or

m = (  a b−K )

use value of m in equation (1) we get

h = (   −b /  b−K   /a  )+a

h = (- ab / b - k) + a

h = - ab + a ( b - k) / b - k

hb - hk = - ab + ab - ak

hb - hk / hk = - ak / hk

or

( b / k) - 1 = - a / h

a / h + b / k = 1

a / x + b / y = 1

Thus the  locus of the point of intersection of lines through a,b and parallel to coordinate axes is 1.