First slide

Equation of line in Straight lines

Question

The condition on a and b, such that the portion of the line $ax + by - 1 = 0$ intercepted between the lines $ax + y = 0$ and $x + by = 0$ subtends a right angle at the origin, is

Moderate

A

$a = b$
B

$a + b = 0$
C

$a = 2 b$
D

$2 a = b$

Solution

Lines $ax + y = 0$ and $x + by = 0$ intersect at $Q (0, 0),$
Hence, if AB subtends right angle at $Q (0, 0),$ then $ax + y = 0$ and $x + by = 0$ are perpendicular to each other so,
$(- a) (- \frac{1}{b}) = - 1$
or $a + b = 0$

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