AP EAMCET20228 Jul 2022Evening ShiftMathematicsStraight LinesActual

The line on which the lines a x+b y=1 and b x+a y=1 (with a 0 b ) intersect for any real values of a and b is

Options

Ax=-y
Bx=2 y
C2 x=y
Dx=y

Correct answer

D. x=y

Step-by-step solution

Lines : a x+b y=1 ...(i) b x+a y=1 ...(ii) [Multiply Eq. (i) by b ] - [Multiply Eq. (ii) by a ] a b x+b^2 y-a b x-a^2 y=b-a y= b-a b^2-a^2 = 1 a+b Put y= 1 a+b in Eq. (i), a x=1- b a+b = a a+b x= 1 a+b Point of intersection of both lines are of type ( 1 a+b , 1 a+b ) . Hence, such points lie on x=y only.

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