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## Main Question or Discussion Point

We're given x^2+2*y^2=1.

so x^2=1-2y^2

now using distance formula

d^2=x^2+y^2

since x^2=1-2y^2, substituting it in the distance formula we get:

d^2=1-2y^2+y^2=1-y^2;

differentiating and then setting the eq to 0 we get;

0=-4y

or y=0. now x^2=1-2y^2=1

so x=+-1

so point having min distance form origin is (+-1,0)

using the distance formula now

d^2=x^2+y^2

d=sqrt(1+0)=1

so x^2=1-2y^2

now using distance formula

d^2=x^2+y^2

since x^2=1-2y^2, substituting it in the distance formula we get:

d^2=1-2y^2+y^2=1-y^2;

differentiating and then setting the eq to 0 we get;

0=-4y

or y=0. now x^2=1-2y^2=1

so x=+-1

so point having min distance form origin is (+-1,0)

using the distance formula now

d^2=x^2+y^2

d=sqrt(1+0)=1