WBJEE · Maths · Circle
If the straight line \(y=m x\) lies outside of the circle \(x^2+y^2-20 y+90=0\), then the value of \(m\) will satisfy
- A \(m < 3\)
- B \(|m| < 3\)
- C \(\mathrm{m} > 3\)
- D \(|\mathrm{m}| > 3\)
Answer & Solution
Correct Answer
(B) \(|m| < 3\)
Step-by-step Solution
Detailed explanation
Hints: \(x^2+m^2 x^2-20 m x+90\) \(\begin{aligned} & x^2\left(1+m^2\right)-20 m x+90=0 \\ & D < 0 \\ & 400 m^2-4 \times 90\left(1+m^2\right) < 0 \\ & 40 m^2 < 360 \\ & m^2 < 9 ;|m| < 3 \end{aligned}\)
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