If the normal at any point on the standard ellipse x^2/a^2 +y^2/b^2 =1,meets its auxillary circle at Q and R such that angle QOR equals to 90 degree ,where O is the centre of the ellipse,then prove that (a^4)+(2 b^4)>=(5a^2 b^2)+(a^3 b).

If the normal at any point on the standard ellipse x^2/a^2 +y^2/b^2 =1

1.	If the normal at any point on the standard ellipse x^2/a^2 +y^2/b^2 =1,meets its auxillary circle at Q and R such that angle QOR equals to 90 degree ,where O is the centre of the ellipse,then prove that (a^4)+(2 b^4)>=(5a^2 b^2)+(a^3 b).
Answer» If the normal at any point on the standard ellipse x^2/a^2 +y^2/b^2 =1,meets its auxillary circle at Q and R such that angle QOR equals to 90 degree ,where O is the centre of the ellipse,then prove that (a^4)+(2 b^4)>=(5a^2 b^2)+(a^3 b).

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If the normal at any point on the standard ellipse x^2/a^2 +y^2/b^2 =1,meets its auxillary circle at Q and R such that angle QOR equals to 90 degree ,where O is the centre of the ellipse,then prove that (a^4)+(2 b^4)>=(5a^2 b^2)+(a^3 b).

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