| If the distance of the point \[P\,\,(x,y)\]from \[A\,\,(a,0)\] is \[a+x,\]then \[{{y}^{2}}\]is equal to |
A) \[2a\,\,x\]
B) \[4a\,\,x\]
C) \[6a\,\,x\]
D) \[8a\,\,x\]
E) None of these
Correct Answer: B
Solution :
| Given, \[AP=a+x\] |
| \[\Rightarrow \]\[\sqrt{{{(x-a)}^{2}}+{{(y-0)}^{2}}}=a+x\] |
| On squaring both sides, we get |
| \[{{(x-a)}^{2}}+{{y}^{2}}={{(a+x)}^{2}}\] |
| \[\Rightarrow \]\[{{x}^{2}}+{{a}^{2}}-2ax+{{y}^{2}}={{a}^{2}}+2ax+{{x}^{2}}\] |
| \[\Rightarrow \]\[{{x}^{2}}+{{a}^{2}}+{{y}^{2}}-{{a}^{2}}-{{x}^{2}}=2ax+2ax\] |
| \[\Rightarrow \]\[{{y}^{2}}=4ax\] |
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