A) Straight line
B) Circle
C) Parabola
D) Ellipse
Correct Answer: C
Solution :
[c] \[\sqrt{{{a}^{2}}{{e}^{2}}+{{b}^{2}}}=c\] (constant) \[\Rightarrow \,\,\,\,\sqrt{{{a}^{2}}-{{b}^{2}}+{{b}^{2}}}=c\] \[\Rightarrow \,\,\,\,\,\,\,c=a\] ??(1) Now, \[h=ae=\sqrt{{{a}^{2}}-{{b}^{2}}}\]b ?....(2) and \[k=\frac{{{b}^{2}}}{a}\] ?...(3) Eliminating b from (2) and (3), we get \[h=\sqrt{{{a}^{2}}-ka}\] Putting \[a=c,\]we get \[{{h}^{2}}={{c}^{2}}-kc\] Thus, the required locus is \[{{x}^{2}}={{c}^{2}}-cy,\]which is parabola.You need to login to perform this action.
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