Question

If the straight line $y = mx$ lies outside of the circle $x^2 + y^2 - 20y + 90 = 0$, then the value of $m$ will satisfy

• A. $m < 3$
• B. $|m| < 3$
• C. $m > 3$
• D. $|m| > 3$

Answer 1

Answer: (B)

The intersection of line and circle is
$x^{2}+m^{2} x^{2}-20 m x+90=0$
$\Rightarrow x^{2}\left(1+m^{2}\right)-20 m x+90=0$
Since, the line lies outside the circle.
$\therefore D < 0$
$\Rightarrow 400 m^{2}-4 \times 90\left(1+m^{2}\right) < 0$
$\Rightarrow 40 m^{2} < 360 \Rightarrow m^{2} < 9$
$\Rightarrow |m| < 3$