Question

A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve $x^2+y^2$ =4 with x+y=a. The set containg the value of 'a' is

• A. {−2,2 }
• B. {−3,3 }
• C. {−4,4 }
• D. {−5,5 }

Answer 1

The correct option is A

{−2,2 }

Lines through (0,0) and through the points of intersection of curve $x^2+y^2$ =4 with the line x + y = a, we get by homogenising the curve with the line

$\frac{x+y}{a}=1\Rightarrow x^2+y^2=4(\frac{x+y}{a}{)}^2$

$\Rightarrow (a^2-4)x^2+(a^2-4)y^2-8xy=0$

We are given these lines are perpendicular to each other

$\therefore$ co-efficent of $x^2+$ coefficent of $y^2=0$

$\Rightarrow a^2-4=0\Rightarrow a=\pm 2$

= {2,-2}