TS EAMCET · Maths · Parabola
\(S \equiv y^2-4 a x=0, S^{\prime} \equiv y^2+a x=0\) are two parabolas and \(P(t)\) is a point on the parabola \(\mathrm{S}^{\prime}=0\). If A and B are the feet of the perpendiculars from P on to coordinate axes and AB is a tangent to the parabola \(\mathrm{S}=0\) at the point \(\mathrm{Q}\left(t_1\right)\), then \(t_1=\)
- A \(t\)
- B \(\frac{t}{4}\)
- C \(\frac{3 t}{4}\)
- D \(\frac{t}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{t}{2}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { } \mathrm{S} \equiv y^2-4 a x=0 \\ & \mathbf{S}^{\prime} \equiv y^2+4 a x=0\end{aligned}\) Let \(\mathrm{P}(t)=\left(\frac{-t^2}{4 a}, t\right) ; \mathrm{So}, \mathrm{A}=\left(\frac{-t^2}{4 a}, 0\right)\) and \(\mathrm{B}=(0, \mathrm{t})\) Line…
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