WBJEE · Maths · Parabola
Let \(A, B\) be two distinct points on the parabola \(y^{2}=4 x\). If the axis of the parabola touches a circle of radius \(r\) having \(A B\) as diameter, the slope of the line \(A B\) is
- A \(-\frac{1}{r}\)
- B \(\frac{1}{r}\)
- C \(\frac{2}{r}\)
- D None of the above
Answer & Solution
Correct Answer
(C) \(\frac{2}{r}\)
Step-by-step Solution
Detailed explanation
Centre of circle \(=\left(\frac{t_{1}^{2}+t_{2}^{2}}{2},\left(t_{1}+t_{2}\right)\right)\) since, circle touch the \(x\) -axis, so equation of tangent is \(y=0\) \(\because\) Radius = Perpendicular distance from centre to the tangent \(\Rightarrow\) Radius…
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