JEE Mains · Maths · STD 11 - 10.2 parabola,ellipse,hyperbola
The locus of the mid points of the chords of the hyperbola \(\mathrm{x}^{2}-\mathrm{y}^{2}=4\), which touch the parabola \(\mathrm{y}^{2}=8 \mathrm{x}\), is :
- A \(\mathrm{y}^{3}(\mathrm{x}-2)=\mathrm{x}^{2}\)
- B \(x^{3}(x-2)=y^{2}\)
- C \(\mathrm{y}^{2}(\mathrm{x}-2)=\mathrm{x}^{3}\)
- D \(x^{2}(x-2)=y^{3}\)
Answer & Solution
Correct Answer
(C) \(\mathrm{y}^{2}(\mathrm{x}-2)=\mathrm{x}^{3}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{T}=\mathrm{S}_{1}\) \(\mathrm{xh}-\mathrm{yk}=\mathrm{h}^{2}-\mathrm{k}^{2}\) \(\mathrm{y}=\frac{\mathrm{xh}}{\mathrm{k}}-\frac{\left(\mathrm{h}^{2}-\mathrm{k}^{2}\right)}{\mathrm{k}}\) this touches \(y^{2}=8 x\) then \(c=\frac{a}{m}\)…
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