Question

14. Find the equation of the straight lines passing through the point (2, 2) and the sum of
the intercepts is 9.
COORDINATE
GEOMETRY Chapter 5 TNSCERT 10

Answer 1

Hi ....dear..
here is your answer!!!

.let the intercepts be a and. b
given that,
a+b= 1...
as we know that if a line intercepts a. and b on axis then it equation will be

x/a. +. y/b=. 1.
bx + ay= ab ....
given that this line line passes through points (2,2) so.. this point will satisfy the equations....
hence putting x= 2 and y= 2 .in above equation ..we..get ,.
2b+ 2a = ab
2(a+b)= ab
2*9 = ab
ab= 18...

...see picture for further solution!!!!...

hope it helped you!!
Regards Brainly Star Community
#shubhendu

Answer 2

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Equation of the line whose

X - intercept is ' a ' and

Y - intercept is ' b ' is

x/a + y/b = 1

*******************************************

Here ,

Sum of the intercepts = 9

Let x - intercept = a ,

y - intercept ( b ) = 9 - a

Required equation ,

x/a + y/(9-a) = 1

This line passing through the

point ( 2 , 2 ).

2/a + 2/( 9 - a ) = 1

=>[ 2( 9 - a ) + 2a]/[a(9-a)] = 1

=> 18 - 2a + 2a = a( 9 - a )

=> 18 = 9a - a²

=> a² - 9a + 18 = 0

=> a² - 6a - 3a + 18 = 0

=> a( a - 6 ) - 3( a - 6 ) = 0

=> ( a - 6 )( a - 3 ) = 0

Therefore ,

a - 6 = 0 or a - 3 = 0

a = 6 or a = 3

i )If a = 6 , b = 9 - a = 9 - 6 = 3

ii ) If a = 3 , b = 9 - 3 = 6

Required equation is

x/6 + y/3 = 1

OR

x/3 + y/6 = 1

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