Question

A line passes through (2,0). The slope of the line, for which its intercept between y = x – 1 and y = –x + 1 subtends a right angle at the origin, is/are

• A.
• B.
• C.
• D.

Answer 1

Answer: (C), (D)

The correct options are
C
D

The joined equation of straight line y = x – 1 and y = –x + 1 is
(x-y-1)(x+y-1) = 0
$\Rightarrow x^2-y^2-2x+1=0$ (1)
Let equation of line passes through (2, 0) is
y = m(x-2) (2)
By homogenizing equation (1) with help of line (2) is
$x^2-y^2-2x\left(\frac{mx-y}{2m}\right)+{\left(\frac{mx-y}{2m}\right)}^2=0$
$\because$ coefficient of $x^2$ + coefficient of $y^2=0$
$\Rightarrow m=\pm \frac{1}{\sqrt{3}}$