Question

If OA, OB are two equal chords of the circle $x^2+y^2-2x+4y=0$ perpendicular to each other and passing through the origin, then the equations of OA and OB are

• A. 3x + y = 0, x + 3y = 0
• B. 3x – y = 0, x – 3y = 0
• C. 3x – y = 0, x + 3y = 0
• D. 3x + y = 0, x – 3y = 0

Answer 1

The correct option is C 3x – y = 0, x + 3y = 0


$Lety=mx,y=-\frac{1}{m}x$ be the equal and perpendicular chords of $x^2+y^2-2x+4y=0$
$\therefore \left|\frac{-2-m}{\sqrt{1+m^2}}\right|=\left|\frac{1-2m}{\sqrt{1+m^2}}\right|\Rightarrow |m+2|=|2m-1|\Rightarrow 2m-1=\pm (m+2)\Rightarrow m=3orm=-\frac{1}{3}\therefore Therequiredlinesarey=3x,y=-\frac{1}{3}x\Rightarrow 3x-y=0,x+3y=0$