JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
\(P\) and \(Q\) are two distinct points on the parabola, \(y^2 = 4x\), with parameters \(t\) and \(t_1\) respectively. If the normal at \(P\) passes through \(Q\), then the minimum value of \(t_1^2\) is
- A \(8\)
- B \(4\)
- C \(6\)
- D \(2\)
Answer & Solution
Correct Answer
(A) \(8\)
Step-by-step Solution
Detailed explanation
\({t_1} = -t - \frac{2}{t}\) \(t_1^2 = {t^2} + \frac{4}{{{t^2}}} + 4\) \({t^2} + \frac{4}{{{t^2}}} \ge 2\sqrt {{t^2}.\frac{4}{{{t^2}}}} = 4\) Minimum value of \(t_1^2 = 8\)
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