JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The locus of the mid-point of the line segment joining the focus of the parabola \(y^{2}=4 a x\) to a moving point of the parabola, is another parabola whose directrix is
- A \(x=-\frac{a}{2}\)
- B \(x =\frac{ a }{2}\)
- C \(x =0\)
- D \(x = a\)
Answer & Solution
Correct Answer
(C) \(x =0\)
Step-by-step Solution
Detailed explanation
\(h=\frac{a t^{2}+a}{2}, k=\frac{2 a t+0}{2}\) \(\Rightarrow \quad t ^{2}=\frac{2 h - a }{ a }\) and \(t =\frac{ k }{ a }\) \(\Rightarrow \quad \frac{ k ^{2}}{ a ^{2}}=\frac{2 h - a }{ a }\) \(\Rightarrow\) Locus of \(( h , k )\) is \(y ^{2}= a (2 x - a )\)…
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