Question

14. Find the equation of the straight lines passing through the point (2, 2) and the sum of
the intercepts is 9.

Answer 1

solution:-

given by:-the equation of the straight lines passing through the point (2, 2) and the sum of
the intercepts is 9.

we have :-

Intercept form:

》(x/a) + (y/b) = 1

Sum of intercept = 9

》 a + b = 9

》 b = 9 - a

The required line is passing through the point (2,2)

》(2/a) + (2/9-a) = 1

》[2 (9 - a) + 2 a]/[a(9 - a)] = 1

》[18 - 2 a + 2a]/9a - a^2 = 1

》18/9a - a^2 = 1

》18 = 9a - a^2

》a^2 - 9 a + 18 = 0

》(a - 3) (a - 6) = 0

》a = 3 and a = 6

Substitute a = 3 and a = 6 in the equation b = 9 - a 

》b = 9 - 3     ,       b = 9 - 6

》b = 6         ,         b = 3

》a = 3 , b = 6

》(x/3) + (y/6) = 1

》(2 x + y)/6 = 1

》2 x + y = 6

》2 x + y - 6 = 0

》a = 6 , b = 3

》(x/6) + (y/3) = 1

》(x + 2y)/6 = 1

》x + 2y = 6

》x + 2 y - 6 = 0

Therefore the required equations are

》2 x + y - 6 = 0

》( x + 2 y - 6 = 0) ans

☆ i hope its help☆

Answer 2

Solution :

*****************************************
Equation of a line whose

x-intercept is a , and y-intercept is b

is

x/a + y/b = 1
*******************************************

Let x - intercept = a

y - intercept ( b ) = 9 - a

Equation ,

x/a + y/( 9 - a ) = 1 which is passing

through ( 2 , 2 ) , then

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 - 3a - 6a + 18 = 0

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

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

a - 3 = 0 or a - 6 = 0

a = 3 or a = 6

Therefore ,

i ) x - intercept = a = 3 ,

y - intercept = b = 9 - 3 = 6

equation ,

x/3 + y/6 = 1

or

ii ) x - intercept = a = 6 ,

y - intercept = b = 9 - 6 = 3

x/6 + y/3 = 1

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