A) (a, ?a)
B) \[(a/2,\ a/2)\]
C) \[(a/2,\ \pm a)\]
D) \[(\pm a,\ a/2)\]
Correct Answer: C
Solution :
Given parabola is \[{{y}^{2}}=2ax\] \ Focus (a/2, 0) and directrix is given by \[x=-a/2\], as circle touches the directrix. \ Radius of circle = distance from the point (a/2, 0) to the line \[(x=-a/2)\]\[=\frac{\left| \frac{a}{2}+\frac{a}{2} \right|}{\sqrt{1}}=a\] \ Equation of circle be \[{{\left( x-\frac{a}{2} \right)}^{2}}+{{y}^{2}}={{a}^{2}}\] ?..(i) also \[{{y}^{2}}=2ax\] ?..(ii) Solving (i) and (ii) we get \[x=\frac{a}{2},\ -\frac{3a}{2}\] Putting these values in \[{{y}^{2}}=2ax\] we get \[y=\pm a\] and \[x=-3a/2\] gives imaginary values of y. \ Required points are\[(a/2,\ \pm a)\].You need to login to perform this action.
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