If the normals at \[P(\theta )\]and \[Q(\pi /2+\theta )\]to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]Meet the major axis at G and g, respectively. Then \[P{{G}^{2}}+Q{{g}^{2}}=\]

\[{{a}^{2}}(1+{{e}^{2}})(2+{{e}^{2}})\]

\[{{b}^{2}}(1-{{e}^{2}})(2-{{e}^{2}})\]

\[{{a}^{2}}({{e}^{4}}-{{e}^{2}}+2)\]

\[{{b}^{2}}(1+{{e}^{2}})(2+{{e}^{2}})\]

If the normals at \[P(\theta )\]and \[Q(\pi /2+\theta )\]to the ellips

1.	If the normals at \[P(\theta )\]and \[Q(\pi /2+\theta )\]to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]Meet the major axis at G and g, respectively. Then \[P{{G}^{2}}+Q{{g}^{2}}=\]
A.	\[{{b}^{2}}(1-{{e}^{2}})(2-{{e}^{2}})\]
B.	\[{{a}^{2}}({{e}^{4}}-{{e}^{2}}+2)\]
C.	\[{{a}^{2}}(1+{{e}^{2}})(2+{{e}^{2}})\]
D.	\[{{b}^{2}}(1+{{e}^{2}})(2+{{e}^{2}})\]
Answer» C. \[{{a}^{2}}(1+{{e}^{2}})(2+{{e}^{2}})\]

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If the normals at \[P(\theta )\]and \[Q(\pi /2+\theta )\]to the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\]Meet the major axis at G and g, respectively. Then \[P{{G}^{2}}+Q{{g}^{2}}=\]

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