min value of a^2/x^2+b^2/y^2=1 from origin is

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Question : If $x=a^{\frac{1}{2}}+a^{-\frac{1}{2}}$, $y=a^{\frac{1}{2}}- a^{-\frac{1}{2}}$, then the value of $(x^{4}-x^{2}y^{2}-1)+(y^{4}-x^{2}y^{2}+1)$ is:
Option 1: 16
Option 2: 13
Option 3: 12
Option 4: 14

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Answer 1

Hello,

Since it's the equation of an Ellipse, So you can assume any parametric coordinate on Ellipse and use the distance formula between the origin and the parametric point. Now differentiate the distance formula expression and equate it to zero to minimize the expression.

Hope this Helps,

Regards,

Arin.

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min value of a^2/x^2+b^2/y^2=1 from origin is

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Question : If $x=a^{\frac{1}{2}}+a^{-\frac{1}{2}}$, $y=a^{\frac{1}{2}}- a^{-\frac{1}{2}}$, then the value of $(x^{4}-x^{2}y^{2}-1)+(y^{4}-x^{2}y^{2}+1)$ is:
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Question : The simplified value of $\small \left (1-\frac{2xy}{x^{2}+y^{2}}\right )\div\left (\frac{x^{3}-y^{3}}{x-y}-3xy\right)$ is:
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Option 4: $\frac{1}{x+y}$

Question : What is the simplified value of $\frac{(x+y+z)(x y+y z+z x)–x y z}{(x+y)(y+z)(z+x)}$?
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