A) \[8{{x}^{2}}9{{y}^{2}}+9y=18\]
B) \[9{{x}^{2}}+8{{y}^{2}}8y=16\]
C) \[8{{x}^{2}}+9{{y}^{2}}9y=18\]
D) \[9{{x}^{2}}8{{y}^{2}}+8y=16\]
Correct Answer: B
Solution :
\[AP+OP+AO=4\] \[\sqrt{{{h}^{2}}+{{(k-1)}^{2}}}+\sqrt{{{h}^{2}}+{{k}^{2}}}+1=4\] \[\sqrt{{{h}^{2}}+{{(k-1)}^{2}}}+\sqrt{{{h}^{2}}+{{k}^{2}}}=3\] \[{{h}^{2}}+{{(k-1)}^{2}}=9+{{h}^{2}}+{{k}^{2}}-6\sqrt{{{h}^{2}}+{{k}^{2}}}\] \[-2k-8=-6\sqrt{{{h}^{2}}+{{k}^{2}}}\] \[k+4=3\sqrt{{{h}^{2}}+{{k}^{2}}}\] \[{{k}^{2}}+16+8k=9({{h}^{2}}+{{k}^{2}})\] \[9{{h}^{2}}+8{{k}^{2}}-8k-16=0\] Locus of P is \[9{{x}^{2}}+8{{y}^{2}}8y16=0\]You need to login to perform this action.
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