Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

from diagram
$\sqrt{2}k=\sqrt{5}\Rightarrow k=\frac{\sqrt{5}}{\sqrt{2}}\Rightarrow \frac{|m+2|}{\sqrt{m^2+1}}=\frac{\sqrt{5}}{\sqrt{2}}\Rightarrow 3m^2-8m-3=0$