A) focus is\[(2,\,\,0)\]
B) latusrectum\[=8\]
C) focus is\[(0,\,\,2)\]
D) latusrectum\[=4\]
Correct Answer: D
Solution :
If the middle point of a chord is \[(\alpha ,\,\,\beta ),\] then \[\alpha =\frac{2{{t}^{2}}+0}{2},\,\,\beta =\frac{4t+0}{2}\] On eliminating\[t\], we get \[\alpha ={{\left( \frac{\beta }{2} \right)}^{2}}\] \[\therefore \]Locus is\[x=\frac{{{y}^{2}}}{4}\] \[\Rightarrow \] \[{{y}^{2}}=4x\] This is the equation of parabola with latusrectum\[4\]
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