Question

The straight lines of the family x(a+b)+y(a-b)=2a (a and b being parameters) are

Answer 1

Answer:

(C) Concurrent at (1,1)

Answer 2

The family of the straight line are concurrent at (1,1).

Given,

The equation = x(a+b)+y(a-b)=2a

To Find,

a = ?

b =?

Solution,

Family of the straight line is = x(a+b)+y(a-b)=2a

= a ( x + y - 2) + b (x-y) = 0

= x+y-2 = 0

= x-y = 2 [Equation 1]

Similarly,

= (x - y) = 0

= x=y [ Equation 2]

From equation 1 and 2,

x-y = 2 = x= 2

(ys get cancelled)

Therefore,

= x+x = 2

x= 1

Putting the value of x= 1 in equation 1,

x-y= 2

1-y = 2

y= 2-1

y = 1

Hence, The family of the straight line are concurrent at (1,1).

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