Question

Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9.

Answer 1

The line is passing through the point ( 2,2 ) and cutting off intercepts on axes whose sum is 9.

The formula for the equation of a line which makes an intercept of a and b unit on the x- axis and y- axis respectively is given by,

x a + y b =1 (1)

It is given that the sum of intercepts equal to 9.

a+b=9 b=9−a

Substitute the value of b in equation (1).

x a + y 9−a =1 x⋅( 9−a )+y⋅a a⋅( 9−a ) =1 x⋅( 9−a )+y⋅a=a⋅( 9−a ) ( 9−a )x+ay=9a− a 2 (2)

Substitute the value of ( x,y ) as ( 2,2 ) in equation (2).

( 9−a )⋅2+a⋅2=9a− a 2 18−2a+2a=9a− a 2 18=9a− a 2 a 2 −9a+18=0

Further simplifying the above equation

a 2 −6a−3a+18=0 a( a−6 )−3( a−6 )=0 ( a−3 )( a−6 )=0 a=3,6

When a=3 .

b=9−a =9−3 =6

Substitute the values of a , b as 3, 6 in equation (1).

x 3 + y 6 =1 2x+y 6 =1 2x+y=6

Now, when a=6 .

b=9−a =9−6 =3

Substitute the values of a , b as 6, 3 in equation (1).

x 6 + y 3 =1 x+2y 6 =1 x+2y=6

Thus, the equation of line passing through the point ( 2,2 ) and cutting of intercepts on axes with sum as 9 are 2x+y=6 or x+2y=6 .